The current ISO week number is shown above. Under ISO 8601, weeks run Monday to Sunday and week 1 is the week containing the first Thursday of January — which is why the first days of a year sometimes belong to week 52 or 53 of the year before.
Why the first-Thursday rule exists
It guarantees that every week belongs entirely to one year and that week 1 always contains at least four days of the new year. The cost is that 1 January is not always in week 1, which surprises people every January — the full explanation is in ISO week numbers explained.
52 or 53 weeks
Most years have 52 ISO weeks; some have 53. Payroll, manufacturing and retail planning all care, because a 53-week year quietly adds a period. Which convention your software uses depends on whether it follows ISO or a Sunday-start scheme — see why weeks start on Monday or Sunday.