Lie theory is essential to many parts of mathematics and theoretical physics, and lie algebras have become a central subject in their own right. This is the first and only book to provide a basic algebraic introduction that has been designed specifically for undergraduates, and that covers all the core material required for all other work in Lie theory. Everything is kept as simple as possible so the only mathematics required is linear algebra, and there are plenty of worked examples and exercises making it ideal for self-study. This will be an essential text for lecturers and undergraduates in mathematics and theoretical physics.