This is an open access book. This textbook contains about 200 fully solved problems in analytical and numerical methods for nonlinear osccillations. These comprise all the end-of-chapter problems in Ali H. Nayfeh and Dean T. Mook's famous textbook Nonliear Oscillations. Mathematical software are adopted to make those solutions more accessible from a graphical point of view. This book can be adopted as a supplement to course work study for graduates or senior undergraduates. Since many exercise problems are adapted from scientific research papers, this book also has a good reference value for scientists and engineers who work in nonlinear vibration.