In this book we consider the problems of estimating convergence and sum of series. Especially series with parameters is the remarkable one. In this book, we extend our remarkable results and offer wonderful methods to consider the convergence and sum of series with parameters.The book contains 4 chapters. Chapter 1 describes basic knowledge concerned with series. Chapter 2 deals with problems of estimating convergence and sum of series with parameters. Chapter 3 describes some hints helpful for the solution of the problems of chapter 2. Chapter 4 gives specific solutions to the problems of chapter 2. The appendix provides some essential graphs to our consideration.We think that this book will be fundamental reference intended for not only students who study mathematical analysis but also students who are eager to have deeper knowledge and readers to get new results.