This book presents a novel two-part framework forpricing all conceivable barrier and lookback optionsin the Black-Scholes world. The first part calls forthe static replication of vanilla and exotic optionprices into simpler European derivative contracts,termed binary options. These are of various ordersand types, and are expressible in terms of themulti-normal distribution function. The second partvalues all types of weakly path-dependent options viathe properties of the Image Method of Buchen, and thevarious extensions developed here. With our methods,the task of pricing any option with either barrierfeatures (whether single, double or exotic), orlookback features, or both, is reducible to pricingequivalent portfolios of the path-independentbinaries we have defined. All pricing presented usingthe framework is accomplished without recourse toformally solving PDEs nor calculating expectations.We use our methods to price all the standard andexotic barrier and lookback options extant in theliterature, as well as to create and price numerousnon-trivial extensions in both the single andmulti-dimensional case.