The Chicago Manual of Style presents two basic documentation systems, the humanities style (notes and bibliography) and the author-date system. Choosing between the two often depends on the subject matter and nature of sources cited, as each system is favored by different groups of scholars.
The humanities style is preferred by many in literature, history, and the arts. This style presents bibliographic information in notes and, often, a bibliography. It accommodates a variety of sources, including esoteric ones less appropriate to the author-date system.
The more concise author-date system has long been used by those in the physical, natural, and social sciences. In this system, sources are briefly cited in the text, usually in parentheses, by the author's last name and date of publication. The short citations are amplified in a list of references, where full bibliographic information is provided.
The University of Chicago Press
http://www.chicagomanualofstyle.org/home.html
Note: Examples in this guide are for the humanities style (i.e. notes and bibliography) of CMOS. For author-date system examples, please use the manual.
Brief Chicago Citation Guide:
https://www.chicagomanualofstyle.org/tools_citationguide.html
The Chicago Manual of Style by 
A Manual for Writers of Research Papers, Theses, and Dissertations by