Please refer to the MuData documentation here.

In the same vein as AnnData is designed to represent unimodal annotated datasets in Python, MuData is designed to provide functionality to load, process, and store multimodal omics data.

MuData
  .obs     -- annotation of observations (cells, samples)
  .var     -- annotation of features (genes, genomic loci, etc.)
  .obsm    -- multidimensional cell annotation, 
              incl. a boolean for each modality
              that links .obs to the cells of that modality
  .varm    -- multidimensional feature annotation, 
              incl. a boolean vector for each modality
              that links .var to the features of that modality
  .mod
    AnnData
      .X    -- data matrix (cells x features)
      .obs  -- cells metadata (assay-specific)
      .var  -- annotation of features (genes, peaks, genomic sites)
      .obsm
      .varm
      .uns
  .uns

MuData can be thought of as a multimodal container, in which every modality is an AnnData object:

from mudata import MuData

mdata = MuData({'rna': adata_rna, 'atac': adata_atac})

If multimodal data from 10X Genomics is to be read, convenient readers are provided by muon that return a MuData object with AnnData objects inside, each corresponding to its own modality:

import muon as mu

mu.read_10x_h5("filtered_feature_bc_matrix.h5")
# MuData object with n_obs × n_vars = 10000 × 80000 
# 2 modalities
#   rna:	10000 x 30000
#     var:	'gene_ids', 'feature_types', 'genome', 'interval'
#   atac:	10000 x 50000
#     var:	'gene_ids', 'feature_types', 'genome', 'interval'
#     uns:	'atac', 'files'

MuData objects represent modalities as collections of AnnData objects. These collections can be saved to disk and retrieved using HDF5-based .h5mu files, which design is based on .h5ad file structure.

import mudata as md

mdata_pbmc.write("pbmc_10k.h5mu")
mdata = md.read("pbmc_10k.h5mu")

It allows to effectively use the hierarchical nature of HDF5 files and to read/write AnnData object directly from/to .h5mu files:

adata = md.read("pbmc_10k.h5mu/rna")
md.write("pbmc_10k.h5mu/rna", adata)