  We present three lectures on heterotic M-theory and a fourth lecture
extending this theory to more general orbifolds. In Lecture 1, Horava-Witten
theory is briefly discussed. We then compactify this theory on Calabi-Yau
threefolds, choosing the "standard" embedding of the spin connection in the
gauge connection. We derive, in detail, both the five-dimensional effective
action and the associated actions of the four-dimensional "end-of-the-world"
branes. Lecture 2 is devoted to showing that this theory naturally admits
static, N=1 supersymmetry preserving BPS three-branes, the minimal vacuum
having two such branes. One of these, the "visible" brane, is shown to support
a three-generation E_6 grand unified theory, whereas the other emerges as the
"hidden" brane with unbroken E_8 gauge group. Thus heterotic M-theory emerges
as a fundamental paradigm for so-called "brane world" scenarios of particle
physics. In Lecture 3, we introduce the concept of "non-standard" embeddings.
These are shown to permit a vast generalization of allowed vacua, leading on
the visible brane to new grand unified theories, such as SO(10) and SU(5), and
to the standard model SU(3)_C X SU(2)_L X U(1)_Y. It is demonstrated that
non-standard embeddings generically imply the existence of five-branes in the
bulk space. The physical properties of these bulk branes is discussed in
detail. Finally, in Lecture 4 we move beyond Horava-Witten theory and consider
orbifolds larger than S^1/Z_2. For explicitness, we consider M-theory orbifolds
on S^1/Z_2 X T^4/Z_2, discussing their anomaly structure in detail and
completely determining both the untwisted and twisted sector spectra.
