Yes. Over 92% of Mexico's population speaks Spanish as their first language—the largest Spanish-speaking population of any country (~130 million).
Mexico's Constitution recognizes Spanish as the de facto national language. The state also recognizes 68 Indigenous language groups (e.g., Nahuatl, Maya, Mixtec, Zapotec) as "national languages" with legal protection, but Spanish is the universal lingua franca of government, education, media, commerce, and daily life.
Regional dialects vary (Northern, Central, Coastal, Yucatecan), but mutual intelligibility is high. Mexican Spanish is distinct from Peninsular Spanish in vocabulary, pronunciation, and grammar (e.g., ustedes for plural "you," seseo, Indigenous loanwords like chocolate, tomato, coyote).