Universal Algebra: partial algebras and homomorphisms

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I'm looking for an accessible introductory text on universal algebra, one which discusses homomorphisms in the context of partial algebras.

I have been recommended the Grätzer book, "Universal Algebra", but I am not sure it is suitable.

I have studied introductory model theory and mathematical logic, and have some knowledge of set theory, but I have never studied algebra of this kind before and am not a mathematician.

What texts or notes, other than the Grätzer, treat of these topics in an accessible fashion?