1 Post-Crisis Fixed-Income Markets -- 1.1 Types of Interest Rates and Market Conventions -- 1.1.1 Basic Interest Rates: Libor/Euribor, Eonia/FF and OIS Rates -- 1.2 Implications of the Crisis -- 1.2.1 Spreads and Their Interpretation: Credit and Liquidity Risk -- 1.2.2 From Unsecured to Secured Transactions -- 1.2.3 Clean Prices Versus Global Prices -- 1.3 The New Paradigm: Multiple Curves at All Levels -- 1.3.1 Choice of the Discount Curve -- 1.3.2 Standard Martingale Measure and Forward Measures Related to OIS Bonds -- 1.4 Interest Rate Derivatives -- 1.4.1 Forward Rate Agreements -- 1.4.2 Fixed and Floating Rate Bonds -- 1.4.3 Interest Rate Swaps -- 1.4.4 Overnight Indexed Swaps (OIS) -- 1.4.5 Basis Swaps -- 1.4.6 Caps and Floors -- 1.4.7 Swaptions -- 2 Short-Rate and Rational Pricing Kernel Models for Multiple Curves -- 2.1 Exponentially Affine Factor Models -- 2.1.1 The Factor Model and Properties -- 2.1.2 Technical Preliminaries -- 2.1.3 Explicit Representation of the Libor Rate -- 2.2 Gaussian, Exponentially Quadratic Models -- 2.3 Pricing of FRAs and Other Linear Derivatives -- 2.3.1 Computation of FRA Prices and FRA Rates -- 2.3.2 Adjustment Factors for FRAs -- 2.4 Pricing of Caps and Floors -- 2.5 Pricing of Swaptions -- 2.6 Relationship with Models from the Literature -- 2.6.1 The Models of Kenyon (2010) and Kijima et al. (2009) -- 2.6.2 The Model of Filipović and Trolle (2013) -- 2.7 Multiple Curve Rational Pricing Kernel Models -- 3 Multiple Curve Heath--Jarrow--Morton (HJM) Framework -- 3.1 Adapting the Classical HJM Approach -- 3.2 Hybrid HJM-LMM Models -- 3.2.1 HJM-LMM Model for the Forward Rates -- 3.2.2 HJM-LMM Model for the Fictitious Bond Prices; 3.3 Foreign Exchange and Credit Risk Analogy -- 3.3.1 Models and No-Arbitrage Conditions -- 3.4 Pricing of Interest Rate Derivatives -- 3.4.1 Linear Derivatives: Interest Rate Swaps -- 3.4.2 Linear Derivatives: Specific Swaps and Ensuing Spreads -- 3.4.3 Caps and Floors -- 3.4.4 Swaptions -- 3.5 Adjustment Factors -- 3.5.1 Adjustment Factor for the Instantaneous Forward Rate Models -- 3.5.2 Adjustment Factor for the HJM-LMM Forward Rate Model -- 4 Multiple Curve Extensions of Libor Market Models (LMM) -- 4.1 Multi-curve Extended LMM -- 4.1.1 Description of the Model -- 4.1.2 Model Specifications -- 4.2 Affine Libor Models with Multiple Curves -- 4.2.1 The Driving Process and Its Properties -- 4.2.2 The Model -- 4.2.3 Pricing in the Multiple Curve Affine Libor Model4.3 Multiplicative Spread Models.