We consider the system of $N$ ($\ge2$) elastically colliding hard balls of
masses $m_1,...,m_N$ and radius $r$ on the flat unit torus $\Bbb T^\nu$,
$\nu\ge2$. We prove the so called Boltzmann-Sinai Ergodic Hypothesis, i. e. the
full hyperbolicity and ergodicity of such systems for every selection
$(m_1,...,m_N;r)$ of the external geometric parameters. The present proof does
not use the formerly developed, rather involved algebraic techniques, instead
it employs exclusively dynamical methods and tools from geometric analysis.