Formation of Topological Defects

In these lectures, I review cosmological phase transitions and the topological aspects of spontaneous symmetry breaking. I then discuss the formation of walls, strings and monopoles during phase transitions including lattice based studies of defect formation and recent attempts to go beyond the lattice. The close connection of defect formation with percolation is described. Open problems and possible future directions are mentioned. (Based on lectures at ICTP, Summer School on Cosmology, July 1997.