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In order to study how biologists calculate the possible genotypes of the offspring I suggest to watch this video:

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Punnett Squares | Genetics | Biology | FuseSchool

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He started considering more traits at the same time, for example colour and seed shape.
Crossing purebred plants producing yellow and round shaped  seeds with purebred plants producing green and wrinkled shaped seeds he obtained dihybrids (di- = two, -hybrid = heterozygous) round and yellow (dominant traits) plants.
He let them self-fertilize naturally and he found that  in the offspring there were four different categories of pea seeds, appearing in a ratio of approximately 9:3:3:1, and the combinations ratio can be predicted considering the two genes independent one from the other.

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States that the alleles of two (or more) different genes get sorted into gametes independently of one another.
The validity of this law is related with the arranegment of the different genes on different chromosomes

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The two alleles segregate during the development of gametes, and each parent’s offspring randomly obtains one factor.

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Mendel took the plants of the "first filial generation" (F1) and let them self-fertilize naturally, they generated the "second filial generation" (F2)
Again he observed the F2 plants phenotype and surprisingly, with a 1:3 ratio, the short trait reappeared.

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Considering plant size, he took tall and short plants from purebred lines, he called them the Parental Generation (P).
Mendel crossed tall purebred plants with short purebred plants creating a new generation: the "first filial generation" (F1).
Observing the F1 phenotype he discovered they were all tall plants.

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gene:"unit of hereditary information, specific section of
a chromosome, located on a fixed position"
allele:"different forms of a gene"
genotype: "the compete set of genetic material of an organism"
phenotype:"the set of an observable traits of an organism"
homozygus:"an organism that have two identical allele for a specific gene"
heterozygous: "an organism that have two different allele for a specific gene"

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He decided to study the trasmission of hereditary traits in pea plants.

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Gregor Johann Mendel (1822-1884):austrian monck, mathematician scientist, still considered the father  of modern genetics.

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States that in an heterozygous gene, one allele will hide the presence of the other allele, rather than both alleles contributing to a phenotype, only one allele will be expressed, which is called dominant, instead the hidden allele is called  recessive.