Part I: Introduction.- 1. Introducing Complex Cardiovascular Physiology.- Part II: Methods.- 2. Symbolic Dynamics, Poincaré Plot Analysis and Compression Entropy Estimate Complexity in Biological Time Series.- 3. Information Decomposition: A tool to Dissect Cardiovascular and Cardiorespiratory Complexity.- 4. Multiscale Entropy: Recent Advances.- 5. Introduction to Complex Systems Analysis with Wavelets.- 6. Intermittency-Driven Complexity in Signal Processing.- 7. Self-Similarity and Detrended Fluctuation Analysis of Cardiovascular Signals.- 8. Time-varying Cardiovascular Complexity with focus on Entropy and Lyapunov Exponents.- 9. Time-frequency analysis of cardiovascular signals and their dynamic interactions.- Part III: Applications.- 10. Measurements of Cardiovascular Signal Complexity for Advanced Clinical Applications.- 11. Applications of Complexity Analysis in Clinical Heart Failure.- 12. Heart Rate Complexity Associated with Diabetic Cardiac Neuropathy.- 13. Applications of Heartbeat Complexity Analysis to Depression and Bipolar Disorder.- 14. Cardiac Autonomic changes in Epilepsy.- 15. Applications of Nonlinear Methods to Atrial Fibrillation.- 16. Complex and Nonlinear Analysis of Heart Rate Variability in the Assessment of Fetal and Neonatal Wellbeing .- 17. ARFIMA-GARCH Modelling of HRV: Clinical Application in Acute Brain Injury.- 18. Age and Gender Dependency of Complexity Measures of Short-term Heart Rate Time Series.- 19. Complexity and Nonlinearities in Cardiorespiratory Signals in Sleep and Sleep Apnea.