How many tenses are there in English?
Two: Present and Past.
Everything else is aspect (progressive, perfect), voice (active, passive), and modality (will, would, ...).
In an alternate point of view, all variants of aspect and voice and of the modals "will" and "would" are considered tenses.
2 "Tenses" x 4 aspects (simple, progressive, perfect, perfect
progressive) x 2 voices x 2 modalities ("will", "would") = 32 tenses.
takes, is taking, has taken, has been taking,
took, was taking, had taken, had been taking,
will take, will be taking, will have taken, will have been taking,
would take, would be taking, would have taken, would have been taking,
is taken, is being taken, has been taken, has been being taken,
was taken, was being taken, had been taken, had been being taken,
will be taken, will be being taken, will have been taken, will have been being taken,
would be taken, would be being taken, would have been taken, would have been being taken
Intransitive verbs cannot form passives, so they have only 16 tenses.
Some authors, curiously, consider the forms with "will" to be tenses, but not the forms with "would".
If you want to include mood (indicative, subjunctive) under the category "tense", you'll have to add even more tenses.
CJ