The aim of this study was to characterize the profile of 47 fatty acids, including conjugated linoleic acid (CLA), 13 fatty acid groups, and 5 Δ(9)-desaturation indices in milk samples from Brown Swiss cows. The genetic variation was assessed and the statistical relevance of the genetic background for each trait was evaluated using the Bayes factor test. The additive genetic, herd-date, and residual relationships were also estimated among all single fatty acids and groups of fatty acids. Individual milk samples were collected from 1,158 Italian Brown Swiss cows and a detailed analysis of fat percentages and milk fatty acid compositions was performed by gas chromatography. Bayesian animal models were used for (co)variance components estimation. Exploitable genetic variation was observed for most of the de novo synthesized fatty acids and saturated fatty acids, except for C4:0 and C6:0, whereas long-chain fatty acids and unsaturated fatty acids (including CLA) were mainly influenced by herd-date effects. Herd-date effect explained large portions of the total phenotypic variance for C18:2 cis-9,cis-12 (0.668), C18:3 cis-9,cis-12,cis-15 (0.631), and the biohydrogenation and elongation products of these fatty acids. The desaturation ratios showed higher heritability estimates than the individual fatty acids, except for CLA desaturation index (0.098). Among the medium-chain fatty acids, C12:0 had greater heritability than C14:0 (0.243 vs. 0.097, respectively). Both C14:0 and C16:0 showed negative additive genetic correlations with the main monounsaturated and polyunsaturated fatty acids of milk fat, suggesting that their synthesis in the mammary gland may be influenced by the presence of unsaturated fatty acids. No correlation was observed between C4:0 and the other short-chain fatty acids (except for C6:0), confirming the independence of C4:0 from de novo mammary fatty acid synthesis. Among the genetic correlations dealing with potentially beneficial fatty acids, C18:0 was positively correlated with vaccenic and rumenic acids and negatively with linoleic acid. Finally, fatty acids C6:0 through C14:0 showed relevant correlations due to unknown environmental effects, suggesting the potential existence of genetic variances in micro-environmental sensitivity. This study allowed us to acquire new knowledge about the genetic and the environmental relationships among fatty acids. Likewise, the existence of genetic variation for most of de novo synthetized fatty acids and saturated fatty acids was also observed. Overall, these results provide useful information to combine feeding with genetic selection strategies for obtaining a desirable milk fatty acids profile, depending on the origin of fatty acids in milk.