Pandas group-by and sum

Use GroupBy.sum:

df.groupby(['Fruit','Name']).sum()

Out[31]: 
               Number
Fruit   Name         
Apples  Bob        16
        Mike        9
        Steve      10
Grapes  Bob        35
        Tom        87
        Tony       15
Oranges Bob        67
        Mike       57
        Tom        15
        Tony        1

Also you can use agg function,

df.groupby(['Name', 'Fruit'])['Number'].agg('sum')

If you want to keep the original columns Fruit and Name, use reset_index(). Otherwise Fruit and Name will become part of the index.

df.groupby(['Fruit','Name'])['Number'].sum().reset_index()

Fruit   Name       Number
Apples  Bob        16
Apples  Mike        9
Apples  Steve      10
Grapes  Bob        35
Grapes  Tom        87
Grapes  Tony       15
Oranges Bob        67
Oranges Mike       57
Oranges Tom        15
Oranges Tony        1

As seen in the other answers:

df.groupby(['Fruit','Name'])['Number'].sum()

               Number
Fruit   Name         
Apples  Bob        16
        Mike        9
        Steve      10
Grapes  Bob        35
        Tom        87
        Tony       15
Oranges Bob        67
        Mike       57
        Tom        15
        Tony        1