This book gives insight into the theoretical backgrounds of optical vortices and their propagation in free space and simple optical systems. The author's theoretical analysis allows full comprehension of recent results and allows a bridge between the mentioned topics. For example, there is a solution for an accelerating beam propagating along an almost half-circle, obtained from a solution for an asymmetric vortex Bessel mode. And vice versa, there is a solution for an optical vortex with accelerating focusing, obtained from a solution for a two-dimensional accelerating Pearcey beam. The book is intended for graduate and postgraduate students studying optics or wave physics.