A high early strength pozzolan cement includes larger sized pozzolan particles and smaller sized hydraulic cement particles which contain tricalcium silicate (e.g., Portland cement). Particles larger than 10 μm are predominantly (50%, 65%, 75%, 85% or 95%) pozzolan particles, and particles smaller than 10 μm are predominantly (50%, 65%, 75%, 85% or 95%) hydraulic cement particles. Excess calcium from the hydraulic cement forms calcium hydroxide available for reaction with the pozzolan particles, optionally in combination with supplemental lime. At least 30%, 40%, 45%, 55%, 65% or 75% of the pozzolan cement (combined pozzolan and hydraulic cement particles) consists of pozzolan, and less than 70%, 60%, 55%, 45%, 35% or 25% consists of hydraulic cement.