Hey I think that you might get a faster answer if you add an f# tag to your question too.
I used the following link to answer your question which has some helpful examples.
This is the solution I came up with. Please note that I added a new column RentedOnDate that actually has a DateTime type that I do the filtering on.
let overview rentedOnDate =
let rentalLog =
__SOURCE_DIRECTORY__ + "/rentallog.csv"
|> Frame.ReadCsv
rentalLog
|> Frame.addSeries "RentedOnDate" (rentalLog.GetSeries<DateTime>("RentedOn"))
|> Frame.filterRowValues (fun row -> row.GetAs<DateTime>("RentedOnDate") = rentedOnDate)
|> Frame.groupRowsByString "Shop"
|> Frame.nest
|> Series.map (fun dtc df ->
df.GetSeries<string>("Title") |> Series.groupBy (fun k v -> v)
|> Frame.ofColumns |> Frame.countValues )
|> Frame.ofRows
// Testing
overview (DateTime.Parse "12/dec/2013 00:00:00")