Progress in low-dimensional topology has been very quick in the last three decades leading to
the solutions of many difficult problems. Among the earlier highlights of this period was
Casson's -invariant that was instrumental in proving the vanishing of the Rohlin invariant of
homotopy 3-spheres. The proof of the three-dimensional Poincaré conjecture has rendered this
application moot but hardly made Casson's contribution less relevant: in fact a lot of modern
day topology including a multitude of Floer homology theories can be traced back to his
-invariant. The principal goal of this book now in its second revised edition remains
providing an introduction to the low-dimensional topology and Casson's theory it also reaches
out when appropriate to more recent research topics. The book covers some classical material
such as Heegaard splittings Dehn surgery and invariants of knots and links. It then proceeds
through the Kirby calculus and Rohlin's theorem to Casson's invariant and its applications and
concludes with a brief overview of recent developments. The book will be accessible to graduate
students in mathematics and theoretical physics familiar with some elementary algebraic and
differential topology including the fundamental group basic homology theory transversality
and Poincaré duality on manifolds.
