There are a few quite large sub-fields, but there are classic textbooks covering most of these. Here are some: For classical enumerative combinatorics, there

There are a few quite large sub-fields, but there are classic textbooks covering most of these. Here are some: For classical enumerative combinatorics, there is Richard Stanley's 'Enumerative Combinatorics'. For graph theory, Diestel's book 'Graph Theory' is popular for introductory courses, and Bollobas' 'Modern Graph Theory' is more advanced and (as the title says) modern. And there is Laszlo Lovasz's fantastic 'Combinatorial Problems and Exercises', which is a collection of problems and answers, and is a great way to get a feel for the subject.