We will analyse how the genetic basis of fitness affects the ability of a population to adapt to changing environmental conditions. Under the assumption that the population would go extinct  in the new environment without evolution, we discuss the concept of evolutionary rescue that occurs when  a few preexisting adapted genotypes reproduce at a rate sufficiently large to avoid population extinction. This adaptation process can be either wanted or unwanted for various reasons, e.g.,  an unwanted consequence of the genetic adaptation of plants  is  herbicide resistance due to the strong selection pressure following  the application of a harmful  substance.\\We provide a time-continuous, polygenic model by means of which different scenarios of emerging resistance or evolutionary rescue can be simulated and analysed in a systematic manner for organisms of different ploidies and for any number of different alleles. Within the model, inheritance at multiple gene loci  is described by a new approach based on tensor products of heredity matrices. This is included as genetic submodel into the time-continuous population model for all possible biotypes. Evolution is acting on the parameters of dose-response curves, i.e., on the mortality rates and thus on the ED50-value. The resulting system of differential equations is analysed with respect to polymorphic equilibria, conditions for evolutionary rescue and the influence of resistance as property of a single genotype compared to resistance as property of a single allel. The different scenarios of resistance development and evolutionary rescue are demonstrated in numerical experiments.