If we speak about airborne software, the main document is the RTCA/EUROCAE DO-178/ED-12 currently at the "C" version:
Software Considerations in Airborne Systems and Equipment Certification: if you want to certify (and thus commercialize) your software for flight, this is the main document to read.
Depending on the scope of the software and the design/development process there might be different supplements (see here):
Software Tool Qualification Considerations
Model-Based Development and Verification Supplement to DO-178C and DO-278
Object-Oriented Technology and Related Techniques Supplement to DO-178C and DO-278A
Formal Methods Supplement to DO-178C and DO-278A
It has been prepared by the RTCA/EUROCAE joint committee and approved by both FAA and EASA under different names, but the content is the same.
As @Greg mentions, these documents are not freely available