  The $\alpha$-particle condensate in nuclei is a novel state described by a
product state of $\alpha$'s, all with their c.o.m. in the lowest 0S orbit. We
demonstrate that a typical $\alpha$-particle condensate is the Hoyle state
($E_{x}=7.65$ MeV, $0^+_2$ state in $^{12}$C), which plays a crucial role for
the synthesis of $^{12}$C in the universe. The influence of antisymmentrization
in the Hoyle state on the bosonic character of the $\alpha$ particle is
discussed in detail. It is shown to be weak. The bosonic aspects in the Hoyle
state, therefore, are predominant. It is conjectured that $\alpha$-particle
condensate states also exist in heavier $n\alpha$ nuclei, like $^{16}$O,
$^{20}$Ne, etc. For instance the $0^+_6$ state of $^{16}$O at $E_{x}=15.1$ MeV
is identified from a theoretical analysis as being a strong candidate of a
$4\alpha$ condensate. The calculated small width (34 keV) of $0^+_6$,
consistent with data, lends credit to the existence of heavier Hoyle-analogue
states. In non-self-conjugated nuclei such as $^{11}$B and $^{13}$C, we discuss
candidates for the product states of clusters, composed of $\alpha$'s,
triton's, and neutrons etc. The relationship of $\alpha$-particle condensation
in finite nuclei to quartetting in symmetric nuclear matter is investigated
with the help of an in-medium modified four-nucleon equation. A nonlinear order
parameter equation for quartet condensation is derived and solved for $\alpha$
particle condensation in infinite nuclear matter. The strong qualitative
difference with the pairing case is pointed out.
