  In this review, we consider the case where electrons, magnetic monopoles, and
dyons become massless. Here we consider the ${\cal N} = 2$ supersymmetric
Yang-Mills (SYM) theories with classical gauge groups with a rank r, SU(r+1),
SO(2r), Sp(2r), and SO(2r+1). which are studied by Riemann surfaces called
Seiberg-Witten curves. We discuss physical singularity associated with massless
particles, which can be studied by geometric singularity of vanishing 1-cycles
in Riemann surfaces in hyperelliptic form. We pay particular attention to the
cases where mutually non-local states become massless (Argyres-Douglas
theories), which corresponds to Riemann surfaces degenerating into cusps. We
discuss non-trivial topology on the moduli space of the theory, which is
reflected as monodromy associated to vanishing 1-cycles. We observe how dyon
charges get changed as we move around and through singularity in moduli space.
