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Let $\iota:(K,\nu)\hookrightarrow(K(x),\mu)$ be a simple purelytranscendental extension of valued fields. In order to study such an extension,M. Vaqui\'e, generalizing an earlier construction of S. Mac Lane, introducedthe notion of Key polynomials. In this paper we define a related notion of\textbf{abstract key polynomials} associated to $\iota$ and study therelationship between them and key polynomials of Mac Lane -- Vaqui\'e.Associated to each abstract key polynomial $Q$, we define the truncation$\mu_{Q}$ of $\mu$ with respect to $Q$ and we study the properties of thosetruncations. Roughly speaking, $\mu_{Q}$ is an approximation to $\mu$ definedby the key polynomial $Q$. We also define the notion of an abstract keypolynomial $Q'$ being an \textbf{immediate successor} of another abstract keypolynomial $Q$ (in this situation we write $Q<Q'$). The main comparison resultsproved in this paper are as follows:(1): An abstract key polynomial for $\mu$is a Mac Lane -- Vaqui\'e key polynomial for the truncated valuation$\mu_{Q}$.(2): If $Q<Q'$ are two abstract key polynomials for $\mu$ then $Q'$is a Mac Lane -- Vaqui\'e key polynomial for $\mu_{Q}$. (3) which, for a monicpolynomial $Q\in K[x]$ and a valuation $\mu'$ of $K(x)$, gives a sufficientcondition for $Q$ to be an abstract key polynomial for $\mu'$. Combined with anearlier result of M. Vaqui\'e, this describes a class of pairs of valuations$(\mu,\mu')$ such that $Q$ is a Mac Lane -- Vaqui\'e key polynomial for $\mu$and an abstract key polynomial for $\mu'$.

Abstract key polynomials and comparison theorems with the key polynomials of Mac Lane -- Vaquie