1 Discontinuity in Economic Theory and Economic Discontinuities.- 1.1 Some Initial Remarks.- 1.2 Discontinuity in the Large and in the Small.- 1.3 The Role of Perspective and the Identification of Discontinuities.- 2 The Mathematics of Discontinuity.- 2.1 General Overview.- 2.2 The Founding Fathers.- 2.3 The Bifurcation of Bifurcation Theory.- 2.4 The Special Path to Fractal Geometry.- 2.5 The Synergetics Synthesis.- 3 Discontinuities in Microeconomic Systems.- 3.1 General Equilibrium Aspects.- 3.2 Discontinuous Competitive Market Dynamics.- 3.3 Discontinuities in Imperfectly Competitive Markets.- 4 Speculative Bubbles and Crashes I: Irrational.- 4.1 Introduction.- 4.2 A Classical View of Irrational Bubbles.- 4.3 Mechanisms of the Speculative Mania.- 4.4 Mechanisms of the Speculative Panic.- 4.5 Varieties of Irrational Bubbles.- 5 Speculative Bubbles and Crashes II: Rational and Semi-Rational.- 5.1 Self-Fulfilling Prophecies as Rational Bubbles.- 5.2 When Are Rational Bubbles Possible?.- 5.3 Price Bubbles in Monetary Economies.- 5.4 Stochastic Rational Bubbles.- 5.5 The Empirical Observability of Bubbles.- 5.6 A Semi-Rational Bubbles Synthesis.- 6 Catastrophe Theory in Macroeconomics.- 6.1 Nonlinear Investment and Business Cycles.- 6.2 Hysteresis of Stagflation.- 7 Chaos Theory and Macroeconomics.- 7.1 Introduction.- 7.2 Sunspots and Regular Cycles in Overlapping Generations Models.- 7.3 Chaotic Cycles in Overlapping Generations Models.- 7.4 Variations on a Theme.- 7.5 Does It Really Exist?.- 7.6 Multiplicity, Indeterminacy, and Worse.- 8 Discontinuity and Capital Theory.- 8.1 The Capital Theory Controversies.- 8.2 Technique Clusters, Discontinuous Technology, and Steady-State Comparisons.- 8.3 But Continuity Does Not Guarantee No Paradox.- 8.4 On the Other Hand Paradox Can Cause Discontinuity.- 8.5 Schumpeterian Discontinuities and Historical Reswitching.- 9 Discontinuous Evolution of Urban Historical Forms.- 9.1 Introduction.- 9.2 Agglomeration and the Formatils