You can find the data on this page Cartografía municipal por distritos a escala 1: 1000, SHP format, ETRS89
The resource is a set of zip files (one for each district of Madrid) which each contain several layers in ESRI Shapefile format.
A description for each layer contained in the zip archives of each district,in spanish language, is available in the file cartografia-distritos-1-1000.csv

We have extracted some of these datasets and created geojson files covering the whole territory.

• buildings.zip (32Mb)
• sidewalks.zip (53Mb)
• footpaths.zip (32Mb)
• bikelanes.zip (3Mb)
• madrid_cycling_network.geojson (3.6Mb)

The data is open data and is licensed under these conditions

The general conditions allow the reuse of data for commercial and non-commercial purposes. You have to cite the origin of the data as Madrid City Council and not suggest the Madrid City Council supports your work

Please read the complete license here in particular the section relative to the *Condiciones generales para la reutilización*