Cellular responses to environmental stimuli are typically thought to be governed by genetically encoded programs. However, recent studies have revealed examples of cells exhibiting adaptive responses and retaining information from past experiences - phenomena akin to learning and memory formation. Here, we demonstrate that melanoma cells can form and maintain cellular memories during the acquisition of drug resistance, exhibiting characteristics of cellular learning. Using a model of a clonal population of metastatic melanoma cell line WM989, we combine dose-escalation experiments, lineage barcoding, and live-cell imaging to investigate cellular adaptation and memory formation. We show that cells exposed to low doses of targeted therapy adapt and become more resistant to higher doses, a process dependent on the AP-1 family of transcription factors. We further expand our experimental paradigm by using dexamethasone as an external signal inducer to test the cells' ability to form memories of induced gene expression states. Through analysis of chromatin accessibility changes and gene expression patterns, we demonstrate that cells can encode the memory of gene expression even after the originating signal disappears. This memory formation is also mediated by AP-1, as shown by inhibition experiments using a JNK inhibitor during the acquisition of resistance. Finally, using a two-color AP-1 reporter system, we show that these memories are encoded in cis. Our findings establish the formation and maintenance of cellular memories as a critical aspect of gene regulation during the development of therapy resistance. This work suggests that cellular learning may be a more general phenomenon than previously recognized, with potential implications for understanding and targeting drug resistance in cancer.