  The massive field-theory approach for studying critical behavior in fixed
space dimensions $d<4$ is extended to systems with surfaces.This enables one to
study surface critical behavior directly in dimensions $d<4$ without having to
resort to the $\epsilon$ expansion. The approach is elaborated for the
representative case of the semi-infinite $|\bbox{\phi}|^4$ $n$-vector model
with a boundary term ${1/2} c_0\int_{\partial V}\bbox{\phi}^2$ in the action.
To make the theory uv finite in bulk dimensions $3\le d<4$, a renormalization
of the surface enhancement $c_0$ is required in addition to the standard mass
renormalization. Adequate normalization conditions for the renormalized theory
are given. This theory involves two mass parameter: the usual bulk `mass'
(inverse correlation length) $m$, and the renormalized surface enhancement $c$.
Thus the surface renormalization factors depend on the renormalized coupling
constant $u$ and the ratio $c/m$. The special and ordinary surface transitions
correspond to the limits $m\to 0$ with $c/m\to 0$ and $c/m\to\infty$,
respectively. It is shown that the surface-enhancement renormalization turns
into an additive renormalization in the limit $c/m\to\infty$. The
renormalization factors and exponent functions with $c/m=0$ and $c/m=\infty$
that are needed to determine the surface critical exponents of the special and
ordinary transitions are calculated to two-loop order. The associated series
expansions are analyzed by Pad\'e-Borel summation techniques. The resulting
numerical estimates for the surface critical exponents are in good agreement
with recent Monte Carlo simulations. This also holds for the surface crossover
exponent $\Phi$.
