Learning and memory are among higher-order cognitive functions that are based on numerous molecular processes including changes in the expression of genes. To identify genes associated with learning and memory formation, here, we used the RNA-seq (high-throughput mRNA sequencing) technology to compare hippocampal transcriptomes between mice with high and low Morris water maze (MWM) cognitive performance. We identified 88 differentially expressed genes (DEGs) and 24 differentially alternatively spliced transcripts between the high- and low-MWM-performance mice. Although the sets of DEGs and differentially alternatively spliced transcripts did not overlap, both were found to be enriched with genes related to the same type of biological processes: trans-synaptic signaling, cognition, and glutamatergic transmission. These findings were supported by the results of weighted-gene co-expression network analysis (WGCNA) revealing the enrichment of MWM-cognitive-performance-correlating gene modules with very similar Gene Ontology terms. High-MWM-performance mice manifested mostly higher expression of the genes associated with glutamatergic transmission and long-term potentiation implementation, which are processes necessary for memory acquisition and consolidation. In this set, there were genes participating in the regulation of trans-synaptic signaling, primarily AMPA receptor signaling (Nrn1, Nptx1, Homer3, Prkce, Napa, Camk2b, Syt7, and Nrgn) and calcium turnover (Hpca, Caln1, Orai2, Cpne4, and Cpne9). In high-MWM-performance mice, we also demonstrated significant upregulation of the “flip” splice variant of Gria1 and Gria2 transcripts encoding subunits of AMPA receptor. Altogether, our data helped to identify specific genes in the hippocampus that are associated with learning and long-term memory. We hypothesized that the differences in MWM cognitive performance between the mouse groups are linked with increased long-term potentiation, which is mainly mediated by increased glutamatergic transmission, primarily AMPA receptor signaling.