Ch. 1. Non integer order circuits and systems. 1.1. Introduction: non integer order physical laws. 1.2. Non inductive transmission line. 1.3. 1/f noise spectra. 1.4. Polarization phenomena. 1.5. Diffusion phenomena. 1.6. Acoustic phenomena. 1.7. Frequency modulation and Bessel function of the first kind -- ch. 2. Main results on non integer order systems. 2.1. Non integer integration: historical notes. 2.2. Preliminaries and definitions. 2.3. Laplace transforms and system's representation. 2.4. General properties of fractional systems. 2.5. Impulse response of a general fractional system. 2.6. Numerical differintegration -- ch. 3. Approximation of non integer order systems via integer order systems. 3.1. Infinite order and non integer order. 3.2. Frequency domain approximation. 3.3. Inverse method: non integer order modeling. 3.4. An example of time domain approximation. 3.5. Genetic algorithms to approximate non integer order system -- ch. 4. Control problem: non integer order feedback controllers. 4.1. Control design: a brief review. 4.2. Non integer order correction. 4.3. The CRONE control. 4.4. Complex integration and evolution of the CRONE. 4.5. Non integer derivative control of the steady state in Chua's circuit. 4.6. [symbol] non integer order controller. 4.7. Non linear system control via [symbol] controller -- ch. 5. Non integer order cellular neural network systems. 5.1. Standard and non integer order CNNs. 5.2. Image processing applications. 5.3. Auto waves in non integer order CNNs -- ch. 6. Circuit design of non integer order chaotic systems. 6.1. Non integer order and chaos. 6.2. The Duffing system. 6.3. Non integer order CNNs and chaos. 6.4. The two-cell CNN circuit -- ch. 7. Conclusion. 7.1. The status of the non integer order system research. 7.2. What it needs to be done. 7.3. Scheme of the book.