What date is this weeks Monday

Try below formula in A2 assuming its for 2017:

=(DATE(2017,1,-2)-WEEKDAY(DATE(2017,1,3))+A1*7)-WEEKDAY(DATE(2017,1,-2-WEEKDAY(DATE(2017,1,3))+A1*7-2))

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On what basis is the WEEKNUM being calculated? From Help file for the function:

Return_type      Week begins on      System
1 or omitted      Sunday                  1
2                  Monday                  1
11                  Monday                  1
12                  Tuesday                  1
13                  Wednesday            1
14                  Thursday            1
15                  Friday                  1
16                  Saturday                  1
17      Sunday      1
21      Monday      2

Once you know the basis of the WEEKNUM calculation you can use the FLOOR or CEILING functions to round the date to the beginning or end of the week and then add or subtract the relevant number of days to get to the Monday of the week.

See attached file with basic option with fixed values in A1 and A2.

Also more flexible options in rows 14 and 15, enter year in B14 and use dropdown or enter day in C14.

Thanks
Rob
Day-of-week.xlsx

Corrected formula for getting Monday's Date without linking so many cells and assuming current year for specified week in A1:

=(DATE(YEAR(TODAY()),1,-2)-WEEKDAY(DATE(YEAR(TODAY()),1,1))+A1*7)-WEEKDAY(DATE(YEAR(TODAY()),1,-2-WEEKDAY(DATE(YEAR(TODAY()),1,1))+A1*7-2))

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I have chosen my suggestion as I feel the logic I have used is simpler to understand.