  In this paper we classify the ten dimensional half BPS solutions of the type
IIB supergravity which have SO(4) X SO(4) X U(1) isometry found by
Lin-Lunin-Maldacena (LLM). Our classification is based on their asymptotic
behavior and causal structure according which they fall into two classes: 1)
those with R X S^3 boundary and 2) those with one dimensional light-like
boundary. Each class can be divided into some subclasses depending on the
asymptotic characteristics of the solutions, which in part specify the global
charges defining the geometry. We analyze each of these classes in some detail
and elaborate on their dual gauge theory description. In particular, we show
that the Matrix Chern-Simons theory which is the gauge theory dual to the LLM
geometries, can be obtained as the effective theory of spherical threebrane
probes in the half BPS sector.
