This monogram is so written that it is self contained for independent study as well and hope it very useful for cognition of maximum independent set, maximum two independent set, maximum two coloured set, minimum 2-nbd covering set, minimum dominating set, all pair shortest path problem. The arrangement and presentation is simple. The chapters are arranged in logical order. The theorems and lemmas have been stated carefully and whenever necessary complete proofs of the theorems and lemmas have been given. The algorithms are illustrated by examples. Also the time and space complexities of all algorithms are investigated. It is hope that the readers will benefit immensely from this monogram.