Infinite Products and Zeta-Regularization.- The Riemann Zeta Function #x03B6;(): a Primer.- Riemann Zeros and Factorizations of the Zeta Function.- Superzeta Functions: an Overview.- Explicit Formulae.- The Family of the First Kind {#x2112; ( )}.- The Family of the Second Kind.- The Family of the Third Kind.- Extension to Other Zeta- and -Functions.- Application: an Asymptotic Criterion for the Riemann Hypothesis.