With a witty and engaging narrative full of jokes and insights and with Grady Klein and Yoram Bauman as our guides, we scale the dual peaks of Mount Derivative and Mount Integral, and from their summits we see how calculus relates to the rest of mathematics. Beginning with the problems of speed and area, Klein and Bauman show how the discipline is unified by a fundamental theorem. We meet such geniuses as Archimedes, Liu Hui, and Bonaventura Cavalieri, who survived the slopes on intuition but prepared us for the avalanche-like dangers posed by mathematical rigor. Then we trek onward, scrambling through limits, extreme values, optimization, and integration, and learn how calculus can be applied to economics, physics, and so much more.