How replicas are formed in Frequency domain when a signal is sampled in Time Domain?
Some people treat sampling in the time domain as the multiplication of a signal $x(t)$ by a periodic impulse train $\sum_n \delta(t-nT)$. Since the Fourier transform of a periodic impulse train is a periodic impulse train $\sum_k \delta\left(f-\frac{k}{T}\right)$ (I might be off by a factor of $T$ here, but the basic idea is correct), and
multiplication in the time domain corresponds to convolution in the frequency domain, 
we get that the Fourier transform of the sampled signal is
$$X(f)\star\sum_k \delta\left(f-\frac{k}{T}\right) = \sum_k X(f)\star\delta\left(f-\frac{k}{T}\right) = \sum_k X\left(f-\frac{k}{T}\right)$$
which is a periodic function of $f$ since $X(f)$ is replicated at intervals of 
$\frac{1}{T}$ Hz along the frequency axis.
If $X(f)$ is bandlimited to $\left(-\frac{1}{2T},\frac{1}{2T}\right)$, the replicas
do not overlap.

Other people resolutely refuse to consider impulse trains and come up
with other, equally valid, means of arriving at the same result.