  In this Chapter, we consider a model of $N$ independent random walkers, each
of duration $t$, and each starting from the origin, on a lattice in $d$
dimensions. We focus on two observables, namely $D_N(t)$ and $C_N(t)$ denoting
respectively the number of distinct and common sites visited by the walkers.
For large $t$, where the lattice random walkers converge to independent
Brownian motions, we compute exactly the mean $\langle D_N(t) \rangle$ and
$\langle C_N(t) \rangle$. Our main interest is on the $N$-dependence of these
quantities. While for $\langle D_N(t) \rangle$ the $N$-dependence only appears
in the prefactor of the power-law growth with time, a more interesting behavior
emerges for $\langle C_N(t) \rangle$. For this latter case, we show that there
is a ``phase transition'' in the $(N, d)$ plane where the two critical line
$d=2$ and $d=d_c(N) = 2N/(N-1)$ separate three phases of the growth of $\langle
C_N(t)\rangle$. The results are extended to the mean number of sites visited
exactly by $K$ of the $N$ walkers. Furthermore in $d=1$, the full distribution
of $D_N(t)$ and $C_N(t)$ are computed, exploiting a mapping to the extreme
value statistics. Extensions to two other models, namely $N$ independent
Brownian bridges and $N$ independent resetting Brownian motions/bridges are
also discussed.
