Mandamus is a judicial remedy that compels a public authority to perform a legally obligated duty and is rare due to its potential to disrupt legal processes. The conditions for issuing mandamus include that the petitioner must have a legal right, there must be a demand for justice that was refused, and it cannot be meant to harass. Types of mandamus include certiorarified mandamus, continuing mandamus, and anticipatory mandamus, each serving unique purposes in ensuring justice.