Indonesian (Bahasa Indonesia) is the official language and lingua franca of Indonesia, in addition to East Timor and places with a significant Indonesian diaspora such as Australia and the Netherlands. With over 230 million speakers, there are a lot of people to talk to in Indonesian. Many universities in Australia and Europe offer Indonesian language courses.
Indonesian is closely related to Malay, and speakers of both languages can generally understand each other to some degree. The main differences are in dialects, pronounciations and loan words: Indonesian has been mainly influenced by Dutch and regional languages like Javanese, Sundanese, etc., while Malay has been mainly influenced by English. Both languages have lots of loan words from Sanskrit, Portuguese/Spanish (historically), Chinese (culinary, daily items), Arabic (especially for religious concepts and vocabularies, Islam and Christian), and English (technology, popular culture, etc.).
Indonesian is relatively young language, generally thought to be born during the Youth Congress in 28 October 1928 (less than 100 years old), but as the only official language in Indonesia since its independence in 1945, for 75+ years it has produced numerous literature and form its specific character to compete with other world languages. Every Indonesian students must learn how to write and speak Indonesian, many as their second language. Indonesian society is highly diglossia (bilingual or trilingual), and many would freely switch back and forth from their mother tongue, Indonesian, and sometimes colloquial Jakartan dialects.
Malay speakers beware, as there are multiple words that are spelled and pronounced the same but convey very different meanings. Among the most familiar are Malay budak (child) to Indonesian budak (slave), Malay percuma (free) to Indonesian percuma (useless), Malay butuh (male genitals) to Indonesian butuh (need), Malay bisa (poison) to Indonesian bisa (can, able to), Malay pusing (to turn) to Indonesian pusing (headache) and Malay banci (a census) to Indonesian banci (sissy, transvestite).
Indonesia uses the Latin alphabet system (26 basic letters and nothing else) and Arabic numerals (0-9), one of the few languages that does that. Indonesian people are used to type with regular US-layout QWERTY keyboard. No other keyboard exist for regional languages, so in turn, every regional language in Indonesia type in computer using Indonesian/English keyboard.
With over 230 million inhabitants dispersed in their local communities, the Indonesian language generally does not serve as a mother tongue, as most of its speakers' first languages are local to their region, such as Javanese, Sundanese, Maduerese, Minang, Acehnese, Balinese, Betawi, Palembang and other large ethnic groups on the west of Indonesia, to the many small ethnic groups of Sulawesi, Maluku, and Papua on the east of Indonesia. Its purpose is to be a language of unification between all the peoples of Indonesia, declared so since the Youth Congress on October 28, 1928.
Indonesian originates from the Malay language usually spoken in central-northeastern Sumatra, which was made famous by the Srivijaya Empire (7th-14th centuries), and then as a working language for trading ("pasar Malay", used in markets alongside the ports). Due to its Malay origin, Indonesian shares a majority of its vocabulary with Malay, but when present-day Malaysia and Indonesia were colonized by different European powers, the trajectories of the two languages started to diverge. After Indonesian, Malaysian and Bruneian independence, the Language Councils of the three countries (Majlis Bahasa Brunei-Indonesia-Malaysia or MABBIM) tried to standardized their languages, resulting in several changes in the spelling of Dutch-influenced Indonesian to match the English-influenced Standard Malay, called Ejaan yang Disempurnakan (Perfected Spelling) of 1972, for example Dutch bigraphs "oe", "dj", "tj", "j" became Indonesian letters "u", "j", "c", and "y". You can still see some of the old spellings in old place names, building names, or even people's names.
Loan words from Dutch/English are absorbed differently in standard Indonesian and standard Malay, where Indonesian mostly opt for transliteration or spelling the words with Indonesian pronounciations, and Malay mostly opt on equivalent words or phonetic transliteration, for example "televisi, polisi, universitas, gubernur, telepon, pulpen" (Indonesian) - "televisyen, polis, universiti, gabenor, telefon, pen founten" (Malaysian) - "televisie, politie, universiteit, gouverneur, telefoon, vulpen" (Dutch) - "television, police, university, governor, telephone, fountain pen" (English). The letters "f" and "v" in Indonesian language and regional languages (such as in the Western part of Java) are sometimes substituted with "p", for example "telepon, pulpen, paham, napas, propinsi, Pebruari, Nopember, aktip" (the first four are considered correct, loaned from telefoon, vulpen in Dutch, and faham, nafas in Arabic, while the last four are incorrect, in English: province, February, November, active).
There is also some variation between local dialects of Indonesian, mostly due to the combination of Indonesian with local mother tongues (regional languages). These local words are mostly used as a slang language (informal conversations), but the Jakartan dialect (influenced by Betawi language) is heavily used on national mass media and thus spoken by children and teenagers consuming those contents. But that being said, all Indonesians can easily switch to the standard language, especially when talking with a foreigner. In written text, school, university, formal emails, speech, conversation between a young person and an old person, conversations between new acquaintances (especially from different ethnicities) standard Indonesian is expected, while in texting, conversation between friends, and other informal context, casual Indonesian is expected.