Anderson was born in Albion, Wisconsin.  He studied at Luther College and Concordia Seminary.  He then served as pastor for various Michigan and Minnesota congregations from 1874-1919.  Abel was the brother of Rasmus B. Anderson, a professor of Scandinavian Studies at the University of Wisconsin, Madison.

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Anderson ble født i Albion, Wisconsin. Han studerte ved Luther College og Concordia Seminary. Deretter jobbet han som prest i flere menigheter i Michigan og Minnesota, fra 1874 til 1919. Abel var bror til Rasmus B. Anderson, professor i skandinaviske språk ved Universitetet i Wisconsin, Madison.