This is a summary of the content of the second part of Deligne's "Hodge Theory, II". The paper discusses filtrations, Hodge structures, and mixed Hodge structures on the cohomology of algebraic varieties. It begins with an introduction to Hodge theory, which describes how the cohomology of a compact Kähler manifold is equipped with a Hodge structure of weight n. The paper then extends this concept to non-compact, non-singular algebraic varieties, introducing mixed Hodge structures that generalize the notion of Hodge structures. The paper presents several key results, including the theorem on mixed Hodge structures and the "lemma of two filtrations". It also discusses the theory of Hodge structures and introduces mixed Hodge structures, which are essential for understanding the cohomology of algebraic varieties. The core of the paper is section 3.2, which defines mixed Hodge structures on the cohomology of algebraic varieties and establishes some degenerations of spectral sequences. The paper also provides various applications of the theory, including the fixed point theorem and semi-simplicity theorem, as well as a complement to previous work. The first section discusses filtrations, including definitions of decreasing and increasing filtrations, and their shifted versions. The paper is essentially algebraic and relies on Hodge theory and Hironaka's resolution of singularities to express the cohomology of a non-singular algebraic variety in terms of that of smooth projective varieties. The paper is written for an audience familiar with algebraic geometry and Hodge theory.This is a summary of the content of the second part of Deligne's "Hodge Theory, II". The paper discusses filtrations, Hodge structures, and mixed Hodge structures on the cohomology of algebraic varieties. It begins with an introduction to Hodge theory, which describes how the cohomology of a compact Kähler manifold is equipped with a Hodge structure of weight n. The paper then extends this concept to non-compact, non-singular algebraic varieties, introducing mixed Hodge structures that generalize the notion of Hodge structures. The paper presents several key results, including the theorem on mixed Hodge structures and the "lemma of two filtrations". It also discusses the theory of Hodge structures and introduces mixed Hodge structures, which are essential for understanding the cohomology of algebraic varieties. The core of the paper is section 3.2, which defines mixed Hodge structures on the cohomology of algebraic varieties and establishes some degenerations of spectral sequences. The paper also provides various applications of the theory, including the fixed point theorem and semi-simplicity theorem, as well as a complement to previous work. The first section discusses filtrations, including definitions of decreasing and increasing filtrations, and their shifted versions. The paper is essentially algebraic and relies on Hodge theory and Hironaka's resolution of singularities to express the cohomology of a non-singular algebraic variety in terms of that of smooth projective varieties. The paper is written for an audience familiar with algebraic geometry and Hodge theory.