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This paper introduces from first principles an abstract algebraic framework of analogical proportions of the form \u2018<jats:italic>a<\/jats:italic>is to<jats:italic>b<\/jats:italic>what<jats:italic>c<\/jats:italic>is to<jats:italic>d<\/jats:italic>\u2019 in the general setting of universal algebra. This enables us to compare mathematical objects possibly across different domains in a uniform way which is crucial for AI-systems. It turns out that our notion of analogical proportions has appealing mathematical properties. As we construct our model from first principles using only elementary concepts of universal algebra, and since our model questions some basic properties of analogical proportions presupposed in the literature, to convince the reader of the plausibility of our model we show that it can be naturally embedded into first-order logic via model-theoretic types and prove from that perspective that analogical proportions are compatible with structure-preserving mappings. This provides conceptual evidence for its applicability. 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