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the physics of elementary particles and forces determined the development of the early universe and thus , of the structure of our world today ( * fig .  1 * ) . according to our present knowledge , three families of quarks and leptons , four fundamental interactions , their respective exchange bosons and a yet - to - discover mechanism to generate particle masses are the ingredients ( * fig .  2 * ) which are necessary to describe our universe , both at cosmic as well as at microscopic scales . three of the four forces are relevant for particle physics at small distances : the strong , the electromagnetic and the weak force . they are described by quantum field theories , quantum chromodynamics ( qcd ) for the strong , quantum - electrodynamics ( qed ) for the electromagnetic and the so - called standard model of the unified electro - weak interactions @xcite . the weakest force of the four , gravitation , is the major player only at large distances where the other three are , in general , not relevant any more : the strong and the weak force are short - ranged and thus limited to sub - nuclear distances , the electromagnetic force only acts between objects whose net electric charge is different from zero .    of the objects listed in * fig . 2 * , only the @xmath2-neutrino ( @xmath3 ) , the graviton and the higgs - boson are not explicitly detected to - date . besides these particular points of ignorance , the overall picture of elementary particles and forces was completed and tested with remarkable precision and success during the past few years , and the data from the lep electron - positron collider belong to the major important ingredients in this field . this lecture reviews selected aspects of standard model physics at lep . the frame of this write - up is not a standard and text - book - like presentation , but rather a collection and reproduction of slides , pictures and tables , similar as presented in the lecture itself . since most of the slides are self - explanatory , the collection is only accompanied by a short , connecting text , plus a selection of references where the reader can find more detailed information . a decade of successful operation of the large electron positron collider , lep @xcite ( * fig .  3 * ) , provided a whealth of precision data ( * fig .  4 * ) on the electroweak and on the strong interactions , through a multitude of @xmath0 annihilation final states ( depicted in * fig .  5 * ) which are recorded by four multi - purpose detectors , aleph @xcite , delphi @xcite , l3 @xcite and opal @xcite . in the phase which is called lep - i `` , from 1989 to 1995 , the four lep experiments have collected a total of about 17 million events in which an electron and a positron annihilate into a @xmath4 which subsequently decays into a fermion - antifermion - pair ( see figs .  4 and  5 ) . since 1995 , the lep collider operates at energies above the @xmath4 resonance , @xmath5 ( lep - ii '' ) , up to currently more than 200 gev in the centre of mass system . the different final states of @xmath0 annihilations can be measured and identified with large efficiency and confidence , due to the hermetic and redundant detector technologies realised by all four experiments . an example of a hadronic 3-jet event , originating from the process @xmath6 with subsequent fragmentation of quarks and gluon(s ) into hadrons , as recorded by the opal detector ( * fig . 6 * ) @xcite , is reproduced in * fig . the basic predictions of the standard model of electroweak interactions , for fermion - antifermion production of @xmath0 annihilations around the @xmath4 resonance , are summarised in * fig . 8 * to * fig .  11 * , see @xcite and recent experimental reviews @xcite for more details . cross sections of these processes are energy ( s``- ) dependent and contain a term from @xmath4 exchange , another from photon exchange as well as a @xmath7 '' interference term ( * fig .  8 * ) . measurements of s - dependent cross sections around the @xmath4 resonance provide model independent results for the mass of the @xmath4 , @xmath8 , of the @xmath4 total and partial decay widths , @xmath9 and @xmath10 , and of the fermion pole cross sections , @xmath11 .    beyond the lowest order born approximation `` , photonic and non - photonic radiative corrections must be considered ( * fig .  9 * ) ; the latter can be absorbed into running coupling constants '' ( * fig . 10 * ) which , if inserted into the born approximation , make the experimental observables depend on the masses of the top quark and of the higgs boson , @xmath12 and @xmath13 . measurements of the fermion final state cross sections as well as of other observables like differential cross sections , forward - backward asymmetries and final state polarisations of leptons ( * fig .  11 * ) allow to extract the basic electroweak parameters . combined analyses of the data of all 4 lep experiments by the lep electroweak working group `` @xcite provide very precise results ( * fig . 12 * ) : for instance , due to the precise energy calibration of lep @xcite , @xmath8 is determined to an accuracy of 23 parts - per - million , and the number of light neutrino generations ( and thus , of quark- and lepton - generations in general ) is determined to be compatible with 3 within about 1% accuracy . from radiative corrections and a combination of data from lep - i and lep - ii , @xmath12 , @xmath13 , the coupling strength of the strong interactions , @xmath1 , the effective weak mixing angle @xmath14 and the mass of the w - boson , @xmath15 , can be determined with remarkable accuracy ( except for @xmath13 which only enters logarithmically ) . a list of the most recent results @xcite is given in * fig . 13 * , where also the deviations of the experimental fits from the theoretical expectations are given by the number of standard deviations ( pull '' ) .    graphical representations of some of these results are given in * fig . 14 * to * fig . 18*. the significance of counting the number of light neutrino families , @xmath16 , from the measurement of the @xmath4 line shape , based on aleph data from the 1990 and 1991 scan period , is displayed in * fig . 14*. the gain in precision of electroweak parameters between 1987 , before the era of lep , and the lep results of 1999 is demonstrated in * fig . 15 * , for the values of the leptonic axial and vector couplings , @xmath17 and @xmath18 .    the fit result of the higgs mass , @xmath13 , ist given in * fig .  16 * , calculated using two different input values for the uncertainty of the hadronic part of the running qed coupling constant , @xmath19 @xcite , together with the exclusion limit from direct higgs production searches , @xmath20  gev ( 95% confidence level ) @xcite .    the measured cross section for @xmath21 pair production , @xmath22 , is presented in * fig . 17 * , together with the standard model prediction and two toy models " which demonstrate the importance of the @xmath23 triple gauge boson vertex and the @xmath24 exchange diagram , see * fig . 5*. a summary of the available measurements ( top ) and indirect determinations , i.e. through radiative corrections ( bottom ) , of the @xmath21 mass is given in * fig . 18*. more results and graphs are available from @xcite and from the home page of the lep electroweak working group @xcite . a short introduction to the development of hadron physics , from the discovery of the neutron to the development of qcd and the experimental manifestation of gluons , is given in * fig . 19*. the basic properties of qcd - in comparison with qed - are summarised in * fig .  20*. the energy dependence of the strong coupling strength @xmath1 , given by the so - called @xmath25-function in terms of the renormalisation scale @xmath26 and the qcd group structure parameters @xmath27 , @xmath28 and @xmath29 , is described in * fig .  21*.    in * fig . 22 * , the anatomy of the process @xmath30  hadrons is illustrated . factorisation is assumed to hold when splitting this process into an electroweak part ( annihilation of @xmath0 into a virtual photon or @xmath4 and subsequent decay into a quark - antiquark pair ) , the development of a parton ( i.e. quark and gluon ) shower described by perturbative qcd , a hadronisation phase which can be modelled using various different fragmentation or hadronisation models , and finally a parametrisation of the decays of unstable hadrons ( according to measured decay modes and branching fractions ) @xcite .    a list of the most prominent qcd topics covered by the lep experiments is given in * fig . 23*. for a more detailed introduction to qcd and hadronic physics at high energy particle colliders see e.g. @xcite ; earlier reviews of qcd tests at lep can be found in @xcite . one of the most prominent qcd - related measurements at lep is the determination of @xmath1 from the radiative corrections to the hadronic partial decay width of the @xmath4 , which is summarised in * fig . 24*. the ratio @xmath31 is a totally inclusive quantity which is independent of hadronisation effects , and qcd corrections are available in complete @xmath32 , i.e. in next - to - next - to - leading order qcd perturbation theory @xcite . the determination of @xmath1 from @xmath33 , however , crucially depends on the validity of the predictions of the electroweak standard model . the basic principles of the physics of hadrons jets , which are interpreted as the footprints of energetic quarks and gluons , and the definition of hadron jets are described in * fig . 25*. the most commonly used jet algorithms in @xmath0 annihilations are clustering procedures as first introduced by the jade collaboration @xcite , and variants of this algorithm @xcite as listed in * tab . 1*.    for these algorithms , relative production rates of @xmath34-jet events ( @xmath34 = 2 , 3 , 4 , ... ) are predicted by qcd perturbation theory , and are therefore well suited to determine @xmath1 and to prove the energy dependence of @xmath1 , see * fig . 26*. in particular , the relative rate of 3-jet events , @xmath35 , is predicted to be proportional to @xmath1 , in leading order perturbation theory . corrections in complete next - to - leading order , i.e. in @xmath36 , are available for these algorithms @xcite . hadronisation effects , however , may significantly influence the reconstruction of jets . this can be seen in * fig . 27 * , where jet production rates are analysed using qcd model ( jetset ) events of @xmath0 annihilation at @xmath37  gev before and after hadronisation , i.e. at parton- and at hadron - level . the @xmath38 of 3-jet reconstruction , i.e. the number of events which are classified as 3-jet both on parton- and at hadron - level , normalised by the number of events classified as 3-jet on hadron level , is displayed in * fig . 28*. the energy dependence of hadronisation corrections to measurements of 3-jet event production rates at fixed jet resolution @xmath39 is analysed in * fig . 29*. from these studies , the original jade and the durham schemes emerge as the most reliable " algorithms to test qcd in jet production from @xmath0 annihilations ( for a comparative study of the newer cambridge algorithm , see e.g. @xcite ) . especially the jade algorithm exhibits small and almost energy independent hadronisation corrections . this allows to test the energy dependence of @xmath1 and thus , of asymptotic freedom , without actually having to determine numerical values of @xmath1 , see * fig . 30 * @xcite . hadronic event shapes ( * fig .  31 * ) are a common tool to study aspects of qcd , and in particular , to determine @xmath1 . for many of these observables , qcd predictions in next - to - leading order ( @xmath36 ) are available @xcite , and for some of them , the leading and next - to - leading logarithms were resummed to all orders @xcite . the results of one such study , performed by l3 @xcite using event shapes of lep - i and lep - ii data plus radiative events at reduced centre of mass energies , is shown in * fig . 32 * , demonstrating the running of @xmath1 . for more details on the determination of @xmath1 from hadronic event shape and jet related observables , see eg . @xcite . a list of high energy particle processes and observables from which significant determinations of @xmath1 are obtained is given in * fig . 33*. the most recent measurements , as an update to the world summary of @xmath1 from 1998 @xcite , are listed in * fig . 34*.    * table 2 * summarises the current status of @xmath1 results . the corresponding values of @xmath40 , where @xmath41 is the typical hard scattering energy scale of the process which was analysed , are displayed in * fig . 35*. the data , spanning energy scales from below 1  gev up to several hundreds of gev , significantly demonstrate the energy dependence of @xmath1 , which is in good agreement with the qcd prediction .    evolving these values of @xmath42 to a common energy scale , @xmath43 , using the qcd @xmath25-function in @xmath44 with 3-loop matching at the heavy quark pole masses @xmath45  gev and @xmath46  gev @xcite , results in * fig . 36 * , demonstrating the good agreement between all measurements . from the results based on qcd calculations which are complete to next - to - next - to - leading order ( filled symbols in fig . 36 ; see also table 2 ) , a new world average of @xmath47}\ ] ] is determined . the overall error is calculated using a method @xcite which introduces an common correlation factor between the errors of the individual results such that the overall @xmath48 amounts to 1 per degree of freedom . the size of the resulting overall uncertainty depends on the method and philosophy used to determine the world average of @xmath49 , see @xcite for further discussion . 99 see textbooks on gauge theories and particle physics , as for instance : + e. leader , e. predazzi , _ an introduction to gauge theories and modern particle physics _ , vols . 1 and 2 , cambridge university press , 1996 ; + c. quigg , _ gauge theories of the strong , weak and electromagnetic interactions _ , benjamin / cummings ( 1983 ) . s. myers , e. picasso , contemp . 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selected topics on precision tests of the standard model of the electroweak and the strong interaction at the lep @xmath0 collider are presented , including an update of the world summary of measurements of @xmath1 , representing the state of knowledge of summer 1999 . 
 this write - up of lecture notes consists of a reproduction of slides , pictures and tables , supplemented by a short descriptive text and a list of relevant references .    0z^0 
 2d_2 2 ^ 2 l 2q^2    mpi - phe/2000 - 02 + january 2000