There are given definitions of M-basis, M-basis with brackets, M-basis with individual brackets and M-basis with permutations and with individual permutations.
The main results are theorems for M-bases in some spaces, on connections between M-bases with individual brackets and with brackets (Theorems 1, 4 and Remark 1), and between M-bases with permutations and with individual permutations (Theorem 3). The paper contains a few very interesting examples.