The Schrodinger equation is the master equation of quantum chemistry. The founders of quantum mechanics realised how this equation underpins essentially the whole of chemistry. However, they recognised that its exact application was much too complicated to be solvable at the time. More than two generations of researchers were left to work out how to achieve this ambitious goal for molecular systems of ever-increasing size. This book focuses on n-mainstream methods to solve the molecular electronic Schrodinger equation. Each method is based on a set of core ideas and this volume aims to explain these ideas clearly so that they become more accessible. By bringing together these n-standard methods, the book intends to inspire graduate students, postdoctoral researchers and academics to think of vel approaches. Is there a method out there that we have t thought of yet? Can we design a new method that combines the best of all worlds?