Ahh, then you want to group by a portion of the date field. You will definitely need to make sure your inv_date is a DATE or DATETIME field, this would be REALLY complicated if it were a VARCHAR.
Then in the SELECT statement you want the customer name and month and year, so it would be something along these lines (plug in your fields as appropriate):
SELECT Customer, YEAR(InvoiceDate) AS IYear, MONTH(InvoiceDate) AS IMonth, SUM(Qty) AS Total
FROM TableName
WHERE InvoiceDate BETWEEN '2010-01-01' AND '2010-12-31'
GROUP BY Customer, YEAR(InvoiceDate), MONTH(InvoiceDate)I usually put the year first so that the sort works out correctly if you span years.
If you want to pull back the Month Name, add the MONTH_NAME(InvoiceDate) function to the SELECT. You will want to leave the MONTH() function in THE GROUP_BY so it sorts numerically instead of alphabetically.