[Name0]
string
string
string
[Name1]
string
string
string
[Name2]
string
string
string

[5й класс]
Иванов
Петров

f = open('txt.txt')
classes = {}
current_class = None
for line in f.readlines():
    if line.startswith('['):
        current_class = line.strip('[]\n')
        classes[current_class] = []
    else:
        classes[current_class].append(line.rstrip())

f.close()

print classes

[5й класс]
Иванов
Петров
[6й класс]
Сидоров
Пупкин
[7й класс]
Шлёпанцев
Коклюшкин

list[0][0] = "Иванов"
list[0][1] = "Петров"

list[1][0] = "Сидоров"
list[1][1] = "Пупкин"

list[2][0] = "Шлёпанцев"
list[2][1] = "Коклюшкин"

in_file = open('test.txt','r')
big_list = []
i = -1
for line in in_file:
    if line.startswith('['):
        big_list.append([])
        i += 1
    else:
        big_list[i].append(line.strip())

big_list = in_file.read().split('[')[1:]
for n, i in enumerate(big_list):
    big_list[n] = i.split('\n')[1:-1]

    big_list[n] = [line for line in i.split('\n')[1:] if line]