  We consider the problem of multi-message private information retrieval (MPIR)
from $N$ non-communicating replicated databases. In MPIR, the user is
interested in retrieving $P$ messages out of $M$ stored messages without
leaking the identity of the retrieved messages. The information-theoretic sum
capacity of MPIR $C_s^P$ is the maximum number of desired message symbols that
can be retrieved privately per downloaded symbol. For the case $P \geq
\frac{M}{2}$, we determine the exact sum capacity of MPIR as
$C_s^P=\frac{1}{1+\frac{M-P}{PN}}$. The achievable scheme in this case is based
on downloading MDS-coded mixtures of all messages. For $P \leq \frac{M}{2}$, we
develop lower and upper bounds for all $M,P,N$. These bounds match if the total
number of messages $M$ is an integer multiple of the number of desired messages
$P$, i.e., $\frac{M}{P} \in \mathbb{N}$. In this case,
$C_s^P=\frac{1-\frac{1}{N}}{1-(\frac{1}{N})^{M/P}}$. The achievable scheme in
this case generalizes the single-message capacity achieving scheme to have
unbalanced number of stages per round of download. For all the remaining cases,
the difference between the lower and upper bound is at most $0.0082$, which
occurs for $M=5$, $P=2$, $N=2$. Our results indicate that joint retrieval of
desired messages is more efficient than successive use of single-message
retrieval schemes.
