Kerygma

Dodd's The apostolic preaching and its developments covers what he thinks the kerygma is in detail, especially early in the book. Not so much the act of preaching but the message. Not so much teaching or exhortation but gospel proclamation.
Thiselton's Hermeneutics Notes that Bultman and Fuchs both make a big deal of this. See subject index therein for kerygma. Bultman is contrasting with "banal teaching."
Baird summarizes in bairdWhatKerygmaStudy1957 that the kerygma proclaims:
- the age of fulfillment (now and not yet)
- came about through JC life, death, resurrection
- Jesus (vindicated by resurrection and exalted to right hand of God
- the HS in the church is manifestation of Christ's power and glory
- the Messianic age of fulfillment will be fully consummated when christ returns (now and not yet)
- an appeal for repentance, the promise of forgiveness and salvation (and invitation to new life and participation in the family of God)
- See 1 Corinthians 15 verses 3-8 and Galatians 1 verses 11-17
See also Paul's recounting of his commission in Acts 26, especially verses 16-23
mcdonaldKerygmaDidacheArticulation1980 is opposed to a strong distinction between kerygma and didache
Reed talks about this in reedBILDEncyclicals2017#Page 15, he says there are 3 things:
- "time is fulfilled"
- Kingdom of God is near
- new of the victory is being proclaimed
- See Ephesians 2
See 1 Corinthians 15:1-6

References

Baird, William. “What Is the Kerygma? A Study of I Cor 15:3-8 and Gal 1:11-17.” Journal of Biblical Literature 76, no. 3 (1957): 181–91. https://doi.org/10.2307/3261567.
Dodd, C. H. (Charles Harold). The Apostolic Preaching and Its Developments. Chicago, New York, Willett, Clark & company, 1937. http://archive.org/details/apostolicpreachi00dodd.
McDonald, James I. H. Kerygma and Didache: The Articulation and Structure of the Earliest Christian Message. Society for New Testament Studies Monograph Series. Cambridge: Cambridge University Press, 1980. https://doi.org/10.1017/CBO9780511520419.
Thiselton, Anthony C. Hermeneutics: An Introduction. Grand Rapids, Mich: W.B. Eerdmans Pub. Co, 2009.