The only free and comprehensive online etymological dictionary of the Spanish language
madre f. (Noun) "mother;" "village elder"
11th cent. From Latin matrem 'id.,' accusative of mater. From Proto-Italic *mātēr 'id.' From Proto-Indo-European *méh2-tēr 'id.' From *meh2-, a root of unknown meaning. Perhaps originally meaning "mother" with *-tēr added by analogy with *ph2ter "father" (see padre).
As a surname de la Madre, perhaps originally given to individuals in reference to the tertiary meaning of madre: terrain cut by a brook or a river. Equally plausible, however, is that it was given in devotion to Mary, the mother of Jesus in Christianity.
Indo-European
Romance
Asturian madre, Portuguese mãe, Galician mai, Catalan mare, French mère, Italian madre
Italic
Oscan maatreís "of the mother," Umbrian matres 'id.,' Faliscan mate "mother," South Picene matereíh "to the mother"
Celtic
Gaulish matir "mother," Celtiberian matrubos "mothers," Old Irish máithir "mother"
Germanic
Old Norse móðir "mother," Old High German muoter 'id.,' Old Dutch muoder 'id.,' Old Saxon mōdar 'id.,' Old Frisian mōder 'id.,' Old English mōdor (English mother)
Albanian
Albanian motër "sister"
Balto-Slavic
Old Church Slavonic mati "mother," Lithuanian mótė 'id.'
Hellenic
Ancient Greek μήτηρ (méter) "mother," Mycenaean ma-te-re 'id.'
Phrygian
Phrygian ματαρ (matar) "mother"
Messapian
Messapian matura "mother"
Armenian
Armenian mayr "mother"
Indo-Iranian
Sanskrit mātár- "mother," Avestan mātar- 'id.'
Tocharian
A mācar "mother," B mācer 'id.'

According to Benveniste (1973), in Indo-European society, the woman who raised the child was called *anna, while the woman with the official title of mother was *māter. This was paralleled in men as well: the man who raised the child was *atta, while the biological father was *pəter.