How can I calculate the total of all elements within a group through the use of group by?

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You can calculate the total of all elements within a group through the use of group by by using the SQL aggregate function SUM(). Here's an example query:

SELECT group_column, SUM(value_column) AS total
FROM table
GROUP BY group_column;

In this query, replace group_column with the column that you want to group by (e.g. category), and replace value_column with the column that contains the values you want to sum (e.g. price). The SUM() function will add up all of the values in each group, and the GROUP BY clause will group the results by the specified column.