Invitation to Discrete Mathematics is at once an introduction and a thoroughly comprehensive textbook for courses in combinatorics and graph theory. It also contains introductory chapters for more specialized courses such as probabilistic methods, applied linear algebra, combinatorial enumeration, and operations research. A lively and entertaining style is combined with rigorous mathematics, and the many illustrations, examples and exercises make the book particularly accessible and user-friendly.
Had to read it in my first year of college, the book still haunts me in my sleep. On a serious note, this is a good discrete math book, that covers all the basics. I found the chapters on graph theory to be particularly well-written, and understandable. It is definitely not an easy read, and occasionally one might get a feeling of reading hieroglyphs, but as long as you stay focused, it is manageable. Also, if you want to self-study discrete maths, I would say that using this book alone would be a torture, but it is a nice supplement to lectures/tutorials that provides a solid and rigorous theoretical base.