This book deals with the application of modern control theory to some important underactuated mechanical systems. It presents modelling and control of the following systems:- the inverted pendulum- a convey-crane system- the pendubot system- the Furuta pendulum- the inertia wheel pendulum- the planar flexible-joint robot- the planar manipulator with two prismatic and one revolute joints- the ball & beam system- the hovercraft model- the planar vertical and take-off landing (PVTOL) aircraft- the helicopter model on a platform- the helicopter modelIn every case the model is obtained in detail using either the Euler-Lagrange formulation or the Newton's second law. We develop control algorithms for every particular system using techniques such as passivity, energy-based Lyapunov functions, forwarding, backstepping or feedback linearization techniques. This book will be of great value for PhD students and researchers in the areas of non-linear control systems, mechanical systems, robotics and control of helicopters. It will help the reader gain experience in the modelling of mechanical systems and familiarize with new control methods for non-linear systems.