Topos theory is the part of category theory that studies categories which are toposes. This includes in particular Grothendieck toposes, i.e. categories of sheaves.
There are always two ways to think of topos theory: as being
topos theory
Introductions include
Ross Street, A survey of topos theory (notes for students, 1978) pdf
Tom Leinster, An informal introduction to topos theory (2010)
A standard textbook is
This later grew into the more detailed
A quick introduction of the basic facts of Grothendieck topos theory is chapter I, “Background in topos theory” in
A standard textbook on this case is
There is also
A gentle basic introduction is
A quick introduction of the basic facts of Grothendieck topos theory is chapter I, “Background in topos theory” in
A survey is in
Colin McLarty, The Uses and Abuses of the History of Topos Theory , Brit. J. Phil. Sci., 41 (1990) (JSTOR) PDF