  By employing a system of interacting stochastic particles as an approximation
of the McKean--Vlasov equation and utilizing classical stochastic analysis
tools, namely It\^o's formula and Kolmogorov--Chentsov continuity theorem, we
prove the existence and uniqueness of strong solutions for a broad class of
McKean--Vlasov equations. Considering an increasing number of particles in the
approximating stochastic particle system, we also prove the $L^p$ strong
convergence rate and derive the weak convergence rates using the Kolmogorov
backward equation and variations of the stochastic particle system. Our
convergence rates were verified by numerical experiments which also indicate
that the assumptions made here and in the literature can be relaxed.
