The branches of science, also referred to as scientific fields or disciplines, are commonly divided into three major groups: formal sciences, natural sciences, and social sciences. Formal sciences study formal systems—such as logic, mathematics, theoretical computer science, information theory, systems theory, decision theory, and statistics—and use a priori methods rather than empirical ones. Natural sciences study natural phenomena, including cosmological, geological, physical, chemical, and biological aspects of the universe; they can be divided into physical sciences and life sciences (biology). Social sciences study human behavior in its social and cultural aspects. Scientific knowledge must be based on observable phenomena and be verifiable by other researchers working under the same conditions, although standards of verifiability may vary within disciplines. Natural, social, and formal sciences constitute the fundamental sciences that underlie interdisciplinary fields and applied sciences such as engineering and medicine. Some specialized disciplines span multiple categories, incorporating terminology and expertise from different fields while retaining their own specializations. Unlike other branches, the formal sciences are not concerned with the validity of theories based on observations in the real world (empirical knowledge), but rather with the properties of formal systems based on definitions and rules. Hence there is disagreement on whether the formal sciences actually constitute a science. Methods of the formal sciences, however, are essential to the construction and testing of scientific models dealing with observable reality, and major advances in the formal sciences have often enabled major advances in the empirical sciences.

Logic is the systematic study of valid rules of inference, i.e., the relations that lead to the acceptance of one proposition (the conclusion) on the basis of a set of other propositions (premises). More broadly, logic is the analysis and appraisal of arguments. It has traditionally included the classification of arguments; the systematic exposition of logical forms; the validity and soundness of deductive reasoning; the strength of inductive reasoning; the study of formal proofs and inference (including paradoxes and fallacies); and the study of syntax and semantics. Historically, logic has been studied in philosophy (since ancient times) and mathematics (since the mid-19th century). More recently, logic has been studied in cognitive science, which draws on computer science, linguistics, philosophy, and psychology, among other disciplines. Information science:
Information science is an academic field primarily concerned with the analysis, collection, classification, manipulation, storage, retrieval, movement, dissemination, and protection of information. Practitioners within and outside the field study the application and use of knowledge in organizations and the interaction between people, organizations, and information systems, aiming to create, replace, improve, or understand those systems.

Mathematics:
Mathematics, in the broadest sense, is a formal science; but traditionally it refers more specifically to the coalition of four areas: arithmetic, algebra, geometry, and analysis, which are, to some degree, the study of quantity, structure, space, and change, respectively.

Statistics:
Statistics is the study of the collection, organization, and interpretation of data. It deals with all aspects of this, including planning data collection through the design of surveys and experiments. A statistician is someone well versed in the thinking necessary for the successful application of statistical analysis; such people often gain this experience through work in a wide range of fields. There is also mathematical statistics, which is concerned with the theoretical basis of the subject. The word "statistics," when referring to the scientific discipline, is singular, as in "Statistics is an art." This should not be confused with the word "statistic," which refers to a quantity (such as the mean or median) calculated from a set of data, whose plural is "statistics" (e.g., "this statistic seems wrong" or "these statistics are misleading").

Systems theory is the transdisciplinary study of systems in general, aimed at elucidating principles that can be applied to all types of systems across fields of research. The term does not yet have a well-established, precise meaning, but systems theory can reasonably be considered a specialization of systems thinking and a generalization of systems science. The term originates from Bertalanffy's General System Theory (GST) and is used in later efforts in other fields, such as Talcott Parsons's action theory and Niklas Luhmann's sociological autopoiesis. In this context, the word "systems" refers specifically to self-regulating systems, i.e., systems that are self-correcting through feedback. Self-regulating systems are found in nature, including the physiological systems of the human body, local and global ecosystems, and the climate.

Decision theory (or the theory of choice, not to be confused with choice theory) is the study of an agent's choices.