1 Introduction -- 2. The art of forgetting 2.1 The formation and retrieval of memories 2.2 Forms of forgetting; first steps of the art. Extinction, repression, discrimination 2.3 Conditioned reflexes 2.4 The rapid forgetting of working memory is intrinsic to its nature 2.5 Brain areas and systems involved in the different types of memory; some basic notions of neuronal function 2.6 Executive functions 2.7 More on the connections between nerve cells 2.8 The forgetting of short- and long-term memory 2.9 Memory and emotions 2.10 More on memory and emotions: endogenous state dependency 2.11 The use and disuse of synapses 2.12 Failure of memory persistence as a form of forgetting? 2.13 Reconsolidation 2.14 Practicing memory 2.15Reading, knowledge, physical exercise, social life, memory and illness 2.16 The art of forgetting: a second approach 2.17 Denial and memory falsification 2.18 Forgetting by large populations 2.19 Surviving through neuronal death 2.20 The famous case of patient H.M. 2.21 When forgetting is not an art: amnesic patients 2.22 Anterograde amnesia by an interference with consolidation 2.23 Neuronal branching and the suppression of branching, neurogenesis and neuronal death as adaptive phenomena 2.24 The acquisition of new memories 2.25 Repression 2.26 A therapeutic use of the art of forgetting 2.27 Accessory memory devices: an adjunct to the art of remembering and to the art of forgetting -- 3. Summing up 3.1 Final comments.