  The field theoretic renormalization group and operator product expansion are
applied to the model of a passive scalar advected by the Gaussian velocity
field with zero mean and correlation function $\propto\delta(t-t')/k^{d+\eps}$.
Inertial-range anomalous exponents, identified with the critical dimensions of
various scalar and tensor composite operators constructed of the scalar
gradients, are calculated within the $\varepsilon$ expansion to order
$\varepsilon^{3}$ (three-loop approximation), including the exponents in
anisotropic sectors. The main goal of the paper is to give the complete
derivation of this third-order result, and to present and explain in detail the
corresponding calculational techniques. The character and convergence
properties of the $\varepsilon$ expansion are discussed; the improved
``inverse'' $\varepsilon$ expansion is proposed and the comparison with the
existing nonperturbative results is given.

Chaotic Dynamics