In this book, the “canard phenomenon” occurring in Van der Pol's equation \(\epsilon \ddot x+(x^2+x)\dot x+x-a=0\) is studied. For sufficiently small \(\epsilon >0\) and for decreasing \(a\), the limit cycle created in a Hopf bifurcation at \(a = 0\) stays of “small size” for a while before it very rapidly changes to “big size”, representing the typical relaxation oscillation. The authors give a geometric explanation and proof of this phenomenon using foliations by center manifolds and blow-up of unfoldings as essential techniques. The method is general enough to be useful in the study of other singular perturbation problems.