I wish to learn nonstandard analysis. Are there any good book recommendations? I'm familiar with the ZFC system, and learnt analysis the classical way. I've found some undergraduate texts, but they are too verbose. 


If there are applications to complex or functional analysis, that would be great.


Thanks in advance.



nonstandard analysis book recommendation
This one sounds like what you want:


[Arkeryd, Cutland and Henson: Nonstandard Analysis, Theory and Applications.](http://books.google.co.uk/books?id=X0BbnEP3jN0C&pg=PA1&lpg=PA1&dq=nonstandard+analysis+cutland&source=bl&ots=B_xdfk9wsQ&sig=iIZA61f8iIvbpE1Wdap0azWtC-c&hl=en&ei=rx6lS_3hEo2OjAeX8tnzCQ&sa=X&oi=book_result&ct=result&resnum=1&ved=0CAsQ6AEwAA#v=onepage&q=&f=false)


I took a course as undergraduate which followed (parts of) this book - I first accompanied it with the more friendly written Goldblatt to get some feeling for the subject, then switched to this one, when I also started finding Goldblatt too "verbose". It found it very well readable.


Cutland has produced other enjoyable writings and there also is [Loeb, Wolff: Nonstandard analysis for the working mathematician](http://books.google.co.uk/books?id=jcjBpRnMiecC&pg=PA168&lpg=PA168&dq=nonstandard+analysis+cutland&source=bl&ots=b4huM_RoNF&sig=PSX8vX6Jl7WWtJqDuptVAfid1qM&hl=en&ei=ih-lS5z2HIvNjAeH1JnuCQ&sa=X&oi=book_result&ct=result&resnum=10&ved=0CCUQ6AEwCTgK#v=onepage&q=nonstandard%2520analysis%2520cutland&f=false), which I haven't read but which follows a very similar agenda at a very similar pace, according to the table of contents.


Enjoy!


