  Singularities, i.e. places of discontinuities of parameters are extremely
general objects appearing in electromagnetic waves and thus are the key to
understanding fundamental wave processes. These structures commonly occur in
purely coherent, highly directional waves, such as laser beams, determining
additional spatial or "`topological"' properties of the wave fields
independently of their propagational dynamics. For instance, topologies of wave
fronts, called phase singularities, add orbital degrees of freedom to
electromagnetic waves. These singularities are common to all types of scalar
waves described only by their intensity and phase distributions. As the
electromagnetic wave is a vector wave, its topological properties generally
depend on all field components leading to complex field patterns in space and
time. These patterns may contain singular points of undefined instantaneous
orientation of the vector field, i.e. the instantaneous field (IF)
singularities. In zero-order paraxial approximation of purely transverse
electromagnetic waves, some instantaneous field distributions may carry
apparent topological monopoles, when the originally source-free wave exhibits
spatial structure associated with the 2D "virtual" sources of electromagnetic
fields. Here we present systematic description of topological singularities in
both electric and magnetic field of the electromagnetic waves in a paraxial
approximation. We also consider the important types of paraxial electromagnetic
waves with complex transverse field structures containing instantaneous field
singularities.
