  (Abridged) While the major contribution to the Cosmic Microwave Background
(CMB) anisotropies are the sought-after primordial fluctuations produced at the
surface of last scattering, other effects produce secondary fluctuations at
lower redshifts. Here, we study the extragalactic foregrounds of the CMB in the
context of the upcoming MAP mission. We first survey the major extragalactic
foregrounds and show that discrete sources, the Sunyaev-Zel'dovich (SZ) effect,
and gravitational lensing are the most dominant ones for MAP. We then show that
MAP will detect (>5 sigma) about 46 discrete sources and 10 SZ clusters
directly with 94 GHz fluxes above 2 Jy. The mean SZ fluxes of fainter clusters
can be probed by cross-correlating MAP with cluster positions extracted from
existing catalogs. For instance, a MAP-XBACs cross-correlation will be
sensitive to clusters with S(94GHz)>200mJy, and will thus provide a test of
their virialization state and a measurement of their gas fraction. Finally, we
consider probing the hot gas on supercluster scales by cross-correlating the
CMB with galaxy catalogs. Assuming that galaxies trace the gas, we show that a
cross-correlation between MAP and the APM catalog should yield a marginal
detection, or at least a four-fold improvement on the COBE upper limits for the
rms Compton y-parameter.
