  We represent and analyze the general solution of the sixth Painleve
transcendent in the Picard-Hitchin-Okamoto class in the Painleve form as the
logarithmic derivative of the ratio of certain $\tau$-functions. These
functions are expressible explicitly in terms of the elliptic Legendre
integrals and Jacobi $\theta$-functions, for which we write the general
differentiation rules. We also establish a relation between the P6-equation and
the uniformization of algebraic curves and present examples.
