The recent publications in the field of information theory and related areas have shown a significant focus on the exploration and extension of fundamental concepts such as entropy, mutual information, and submodular functions. A notable trend is the development of novel representations and interpretations of these concepts, which not only deepen our understanding but also open new avenues for their application in privacy measures and data compression. The research has also seen advancements in the generalization of classical inequalities and the introduction of new functions that extend the scope of traditional information measures. These developments are characterized by a rigorous mathematical approach, aiming to establish precise conditions and properties that enhance the applicability and interpretability of information-theoretic measures.nnAmong the noteworthy contributions, the exploration of $alpha$-mutual information stands out for its innovative approach to privacy leakage measures. The work on entropic versions of Bergstru00f6m's and Bonnesen's inequalities is remarkable for strengthening and generalizing well-known inequalities in information theory. The combinatorial perspective on information content and entropy offers a fresh viewpoint that bridges traditional entropy concepts with combinatorial methods. The investigation into the fractional subadditivity of submodular functions and its implications for equality conditions is particularly significant for its broad applicability across various special cases of submodular functions. Lastly, the characterization of the rate-distortion-perception function for Bernoulli vector sources and the study of discrete layered entropy contribute valuable insights into the efficient compression of sources and the approximation of Shannon entropy, respectively.