Theory and guides of using linear models with fixed and random effects is elaborated, which is useful for evaluation different types of experiments and evaluation of populations of animals, including large nation-wide files. Different types of examples with single-trait ant multi-trait variables, direct and maternal effects and longitudinal data of test-day-models are presented. Are included models with only fixed effects (LSM) and with mixed fixed and random effects (BLUP, REML). For random effect of animals are calculated with BLUP-Animal Model expected breeding values (EBV) and genomic enhanced breeding value (GEBV). For prediction of GEBV are used methodologies with genetic regression coefficients RRBLUP, with genomic relationship GBLUP and singles step procedure ssGBLUP. Calculations are by own programing in environment SAS and with using of software available in internet BLUPF90-family and DMU. For different examples and used software are prepared files of parameters.