Free online (third) edition of Diestel's Graph Theory book is available here. This is one of the first books on Graph Theory, I read. Graph Theory with Applications by Bondy and Murty is another good introductory book. Its free online edition is here. I find lots of references to this book in graph theory and discrete math publications. Douglas West's Book is another excellent introductory book. Together these three books make an invaluable addition to your theory books library. I like the exercises in these books. If you read the chapters carefully you can come up with elegant and beautiful proofs for the exercises. If books have taglines, I would call these books Graph Theory: Fun Unlimited.