The main objective of bringing out this monograph is, unlike so many others, is the passion towards the subject by name mathematics. While being passionate for this subject, I thought of making my passion should be useful to, at least some people who are crazy about mathematics just like me. This monograph gives and emphasis on recurrence relations and it is tag lined as Methods to Madness, not to make a people mad but to prove that it can make you fall in love with mathematics madly. A large number of problems have been discussed and the solutions are presented in a way that they can be of great help to researchers. What is more important is that all these problems are very much useful for researchers and scholars as they are solved in a very lucid and comprehensive manner. We are hopefully the solutions will help you for your endeavors, since new techniques and methods are adopted for bringing out the solutions.