This thesis deals with polynomial Liénard equations of type , i.e. planar vector fields associated to a scalar second order differential equation , with and olynomials of respective degree and . The functions and are called “friction term” and “forcing term”, respectively. It is shown that, besides compactifying the phase plane, or the Liénard plane, one can also compactify and desingularize the space of Liénard equations of type for each separately, by adding both singular perturbation problems and Hamiltonian perturbation problems. Polynomial Liénard equations occur as models or at least as simplifications of models in many domains in science. For an example, during the development of radio and vacuum tube technology, Liénard equations were intensely studied as they can be used to model oscillating circuits. The Van der Pol oscillator equation is a Liénard equation, as given below: As put forward by Smale in his list of problems for the 21st century (see [8]) they are also a good starting point to try to solve the second part of Hilbert’s 16th problem asking for a uniform upperbound only depending on the degree for the number of limit cycles of polynomial planar vector fields