How to group dates by week?

In addition to Jon's answer you can get the date of the first day in the week then group by that date.

To get the date of the first day in the week. you can use this code:

public static class DateTimeExtensions
{
    public static DateTime StartOfWeek(this DateTime dt, DayOfWeek startOfWeek)
    {
        int diff = dt.DayOfWeek - startOfWeek;
        if (diff < 0)
        {
            diff += 7;
        }
        return dt.AddDays(-1 * diff).Date;
    }
}

then you can group by the first date of the week like this:

var consignmentsByWeek = from con in consignments
                         group con by con.Datedate.StartOfWeek(DayOfWeek.Monday);

Hesitant though I am to disagree with as esteemed an answerer I believe the accepted answer here is wrong, and this is not fundamentally a question of projecting to a week of year value.

GetWeekOfYear(), and the concept in general, is about assigning index values to weeks within a year according to some agreed standard. It is not suitable for placing dates into groups of seven adjacent days as I believe the questioner requires.

Not only will use of GetWeekOfYear() as proposed result in groups of fewer than seven days at the end of many years, but worse still, as the various standards supported by GetWeekOfYear() will often apportion the first days of a year to the last week of the previous year, and yet the GetWeekOfYear() result contains only the integer week index with no reference to associated year, grouping by new { Year = date.Year, weekProjector(date) } or date.Year + "-" + weekProjector(date) in the questioner's year would see January 1st 2011 grouped in with Christmas Day through to New Year's Eve twelve months later that same year.

So I would argue that the original question is fundamentally one of projecting not to a week of year value but to a week of all time value, "week beginning y/m/d" you might say, so grouping need only be done by the first day of the week, i.e. (assuming you're happy to default to Sunday) simply:

group by date.AddDays(-(int)date.DayOfWeek)

The fundamental question here is how to project a DateTime instance into a week of year value. This can be done using by calling Calendar.GetWeekOfYear. So define the projection:

Func<DateTime, int> weekProjector = 
    d => CultureInfo.CurrentCulture.Calendar.GetWeekOfYear(
         d,
         CalendarWeekRule.FirstFourDayWeek,
         DayOfWeek.Sunday);

You can configure exactly how the "week number" is determined by tweaking the parameters in the method call. You can also decide to define the projection as e.g. an extension method if you prefer; this does not change the essence of the code. In any case, you are then ready to group by week:

var consignmentsByWeek = from con in consignments
                         group con by weekProjector(con.Date);

If you also want to constrain the output to consigments between two specific dates, just add an appropriate where clause; the grouping logic does not change.