Are there enough interesting results that hold for general locally ringed spaces for a book to have been written? If there are, do you know of a book? If you do, pelase post it, one per answer and a short description.


I think that the tags are relevant, but feel free to change them.


Also, have there been any attempts to classify locally ringed spaces? Certainly, two large classes of locally ringed spaces are schemes and manifolds, but this still doesn't cover all locally ringed spaces.



A book on locally ringed spaces?
In addition to the examples mentioned in the question, of manifolds and schemes, other commonly occuring types of locally ringed spaces are formal schemes and complex analytic spaces. 


I don't know how extensive the taxonomy of locally ringed spaces is. For example,
if $A$ is a local ring, we can form the locally ringed space consisting of a single point,
with $A$ sitting on top of it. These are the topologically simplest locally ringed spaces
(after the empty space).
If $A$ is a field, one obtains a scheme. If $A$ is a complete local ring, one obtains a formal scheme. In general, this doesn't fit into any particular taxonomic grouping that I know of.


Incidentally, it might be worth mentioning that the various taxonomic classes can interact:
for example, analytification of schemes over ${\mathbb C}$ is conveniently described in terms of 
maps (in the category of locally ringed spaces) to complex analytic spaces.


