Potential Functions for Signals and Symbolic Sequences -- Braverman's Spectrum and Matrix Diagonalization versus iK-Means: A Unified Framework for Clustering -- Compactness Hypothesis, Potential Functions, and Rectifying Linear Space in Machine Learning -- Conformal Predictive Distributions with Kernels -- On the Concept of Compositional Complexity -- On the Choice of a Kernel Function in Symmetric Spaces -- Causality Modeling and Statistical Generative Mechanisms -- One-Class Semi-Supervised Learning -- Prediction of Drug Efficiency by Transferring Gene Expression Data from Cell Lines to Cancer Patients -- On One Approach to Robot Motion Planning -- Geometrical Insights for Implicit Generative Modeling -- Deep Learning in the Natural Sciences: Applications to Physics -- From Reinforcement Learning to Deep Reinforcement Learning: An Overview -- A Man of Unlimited Capabilities -- Braverman and His Theory of Disequilibrium Economics -- Misha Braverman: My Mentor and My Model -- List of Braverman's papers published in the "Avtomatika itelemekhanika" journal, Moscow, Russia, and translated into English as "Automation and Remote Control" journal.

This state-of-the-art survey is dedicated to the memory of Emmanuil Markovich Braverman (1931-1977), a pioneer in developing the machine learning theory. The 12 revised full papers and 4 short papers included in this volume were presented at the conference "Braverman Readings in Machine Learning: Key Ideas from Inception to Current State" held in Boston, MA, USA, in April 2017, commemorating the 40th anniversary of Emmanuil Braverman's decease. The papers present an overview of some of Braverman's ideas and approaches. The collection is divided in three parts. The first part bridges the past and the present. Its main contents relate to the concept of kernel function and its application to signal and image analysis as well as clustering. The second part presents a set of extensions of Braverman's work to issues of current interest both in theory and applications of machine learning.The third part includes short essays by a friend, a student, and a colleague.