Can different mutations lead to the same allele? In my genetics books, I always see alleles referenced as, eg. Aa where A = dominant and a = recessive, but are these strictly binary phenotypes? Since there are an infinite number of mutations that could theoretically take place, wouldn't there be an infinite number of alleles? Eg (not an actual biological phenomenon but just as an example) A1C on chomosome 3 leads to allele a1, A1T leads to allele a2, etc.
You are looking at high school biology books. if that. I'd be shocked if a high school text didn't mention blood group genes, for instance.
The simple genetics that Mendel elucidated only applies to a very small number of situations.
In real life, very few situations are explained by the interactions of only two different alleles, one of which is classically dominant to the other, within a single gene.
So sure, you could have many alleles which break a gene, but where the presence of one working allele is enough to be functionally indistinguishable from having two working copies. You could also have slight sequence differences that are functionally identical.
Here's a random example; all the variants ensembl knows about for a random gene. Note that these are only variants which have been found, obviously private individuals and families might have their own variants that are not documented
Most of these are in the 3' UnTranslated Region, and likely have no functional significance.