anti-Markovnikov addition
Anti-Markovnikov addition is any addition to an alkene where the pieces end up the 'wrong way round' compared with the Markovnikov prediction — the hydrogen lands on the more-substituted carbon and the other group on the less-substituted one. It is not a violation of chemistry; it simply happens when the reaction does not go through the usual carbocation, so a different rule decides the orientation.
There are two famous routes. The first is radical hydrobromination: HBr in the presence of peroxides (or light) adds via a chain of radicals rather than ions. A bromine radical adds first, and it adds to whichever carbon leaves the more stable carbon radical (the more substituted one) — which is the opposite carbon from where Br would land ionically, so Br ends up on the less-substituted carbon. The second is hydroboration-oxidation, where boron (the electron-poor atom) attaches to the less-hindered, less-substituted carbon and is later replaced by OH, putting the hydroxyl anti-Markovnikov.
Anti-Markovnikov methods are prized precisely because they reach products the standard ionic additions cannot. Want the hydroxyl on the terminal carbon of a 1-alkene? Markovnikov hydration gives the internal alcohol, but hydroboration-oxidation gives the terminal one. Having both orientations available — pick your conditions, pick your regiochemistry — is what makes alkenes such versatile synthetic starting points.
Adding HBr to propene normally gives 2-bromopropane (Markovnikov), but adding HBr with a peroxide catalyst gives 1-bromopropane (CH3-CH2-CH2-Br), the anti-Markovnikov product, because a radical chain replaces the ionic mechanism.
Change the mechanism (radical or hydroboration) and the regiochemistry flips.
The peroxide effect works only for HBr, not HCl or HI: the radical chain is energetically favourable for bromine but not for the others, so adding peroxides to HCl will not give anti-Markovnikov product.