Theme: The Son shares his inheritance with all those who trust in him; pursue the unity that he has won

What do elementary things refer to?
Most likely, 'elementary things' refers to the rules and regulations by means of which both Jews and Gentiles attempted to achieve salvation/ensure future life with God in glory. In context, Paul is primarily referring to Jews and Mosaic law (cf. Galatians 3:22-23), secondarily to the Gentile believers (philosophical teachings).