Expense reporting, get values from column and return only unique values somewhere else

Question

i would like check a column for the values it contains (expense categorizations) and then return a list of only the unique values somewhere else in a vertical list. So "gasoline" may be listed 12 times in the reference list but in my result listing i would expect it to only show up once. If there is a way to do this then I would also like to know how empty cells are handled.
I will then be applying a SUMIF to the returned list to get totals for all the unique categorization a have specified.
Thank you for your time.

Answer 1

Deleting the first row made your $F$2 become $F$1.
Explaining how a formula works is not so easy to do. I'll try, but the best way is to read up on the formulas and piece it all together.  There's nothing fancy or tricky going on here.
The "active ingredient" in the formula is this piece: OFFSET('Table 1-2'::$F$1,SMALL('Table 1-2'::G,ROW()−1)−1,0)
ROW() returns the row number of the cell that has the formula in it. It is an easy way to get an ever increasing number for the formula. The other way would be to have another column with 1,2,3,4, etc. in it.  So, ROW() will return the number 1 if the formula is in row 1, will return the number 2 in row 2, etc.
SMALL(range, n) returns the nth smallest number from the given range of numbers.  So, for the formula  in row 2, SMALL('Table 1-2'::G, ROW()−1) becomes SMALL('Table 1-2'::G, 1) which will return the 1st smallest number from the G column of Table 1-2.  In the 3rd row it would return the 2nd smallest number. Etc.  And remember that those numbers it is returning are the row numbers of your unique values in Table 1-2.
OFFSET(base, row offset, column offset) is a way of  referencing a cell.  For instance, OFFSET($F$1,1,0) would be one row down from cell F1. OFFSET($F$1,2,3) would be two rows down and three columns to the right of cell F1.  The SMALL formula has given you the row number for a unique value in your Table 1-2.  To reference the correct row, the row offset from F1 needs to be one less than that number (an offset of 0 = cell F1. An offset of 1 = cell F2, etc.). The column offset is zero.