The rule for next Monday and the next Monday is simple.
Next Monday refers to the Monday that comes after the present one (US)/ the Monday that comes after the present one or previous one (British)
If you refer to a different Monday in the future or in the past, you have to use 'the'.
A Monday in the past: "When we arrived, we were told that the airport would open only the next Monday."
A Monday in the future that's later then next Monday: "We will be arriving there in two week's time and the crew will follow the next Monday."
Likewise for the next year, the next season, etc...
When we talk about days of the week, weeks, months, years, seasons or
public holidays in the future in relation to now, we use next without
the and without a preposition:
- I have an appointment with the dentist next Wednesday morning.
(Not: … the next Wednesday morning).
- Are you working next week?
(Not: Are you working on next week?)
- Next year will be our fortieth wedding anniversary.
- We’re going to plant some new flowers next spring.
To refer to the future, we can use the next few hours,
the next two days, the next six months, etc.:
- I’ll finish the work in the next few days. You can pay me then.
- We’ll be home for the next three weeks,
then we’re going away to France for two weeks.
When we talk about times in the past or future not related to now, we
normally use the. However, in informal situations, we can omit the
when we talk about the past:
- The next day we travelled to the ancient city of Qom.
- We’re going to spend the first night in Oslo,
then the next day we’ll fly to Narvik.
- Two policemen grabbed me.
Next minute, I was arrested and thrown into a van.
Page 319, English Grammar Today, Cambridge University Press, ©2011
See also section 4.4.6 (c), Page 281- Longman Grammar of Spoken and Written English, ©1999. The article is too long to quote here.