Archaeoastronomy is the study of beliefs and practices relating to the sky in the past, especially in prehistory, and the uses to which people’s knowledge of the skies was put.
Journals, present and past
Cultural astronomy is the combination of archaeoastronomy and ethnoastronomy, which relates to contemporary cultures.
Professional bodies
The 3-volume Springer Handbook contains 217 chapters on themes, issues, methods and practice, and case studies by authors from around the world.
You might also be interested in some of the materials to be found on cultural-astronomy.com.
The UNESCO–IAU Portal to the Heritage of Astronomy contains a wide range of examples of different types of astronomical heritage together with information relevant to its protection, conservation, evaluation, management and promotion.