When a phase transition occurs in the early universe, the alignment of the spontaneous symmetry breaking expectation value may be different in adjacent causal domains. In that case, topologically stable objects such as domain walls, cosmic strings and magnetic monopoles, referred to as ‘topological defects’, can be formed. In this chapter, the authors develop the theory of domain walls, cosmic strings and magnetic monopoles in turn. One-dimensional topological defects (cosmic strings) can also be produced by phase transitions in the early universe. The simplest example of a cosmic string may be derived from the Lagrangian density for a complex scalar field. The local cosmic string or gauge string carries magnetic flux. To calculate the gravitational field due to a cosmic string, the energy–momentum tensor produced by the string is required.