FAA has worked with ASTM International to develop consensus standards for light-sport aircraft. These consensus standards satisfy the FAA's goal for airworthiness certification and a verifiable minimum safety level for light-sport aircraft" (Consensus Standards, 2018). Note that some standards on this list have been superseded or replaced with a new version, OR withdrawn.
The FAA's aircraft certification processes assure safe aircraft designs. Airworthiness is ultimately the required design standard for this course. You will focus on the part 23 and part 25 standards for fixed wing aircraft). Parts 21, 39, 43, and 91 also are relevant but are not dealt with to the same degree in the course. They are less about design and more about maintenance and operation.
MIL-SPEC
MIL-SPEC stands for "military specifications." There are thousands of them, with many that refer to airplane designs and the processes and materials used to manufacture them. MIL-SPECs are often (but not always) available for free download on the web. Use the ASSIST site below to search for relevant MIL-SPECs by keyword or document ID (for example MIL-B-83787).
ASSIST Quick Search is a public website that lets users search for defense and federal specifications and standards, military handbooks, commercial item descriptions, data item descriptions, MS detail drawings, Qualified Product Lists (QPLs), and related technical documents prepared in accordance with the policies and procedures of the Defense Standardization Program (DSP). In most cases, users may download documents that have been cleared for public release.