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Abstract. Motivated by certain classical conjectures over number fields that logarithms of alge-braic numbers should be algebraically independent over Q whenever they are linearly independent over Q, G. Anderson developed machinery called t-motives to attack this problem over function fields. Later, as a way of constructing explicit logarithms of algebraic numbers in the function field setting, Anderson developed a technique that he referred to as log-algebraicity. Due to the monumental work of M. Papanikolas we know now that Andersons machinery of t-motives works, and further we have the following remarkable theorem, due to Papanikolas: If λ1,..., λr are (Carlitz) logarithms of numbers which are algebraic over the rational function field K with coefficients in a finite field, and if λ1,..., λr are linearly independent over K, then they are algebraically independent over the algebraic closure of K. We shall use transcendence as motivation for studying Anderson’s log-algebraicity in the sim-plest case of polynomial rings over finite fields. We will introduce the Carlitz module and related functions, and we will draw analogies with classical constructions as we move along. This set of notes is intended for a general mathematical audience, in particular, non-number theorists