Included in this book is proof of van der Waeroen's 1926 conjecture on permanents, Wilson's theorem on asymptotic existence, and other developments in combinatorics since 1967. Also covered is coding theory and its important connection with designs, problems of enumerations and partition, along with fundamentals in addition to latest advances, with illustrative problems at the end of each chapter. Enlarged appendixes include a longer list of block designs.