Interslavic (Medžuslovjansky / Меджусловјанскы), which started in 2006 under the name Slovianski, is a constructed language designed to be used as an auxiliary language between speakers of different Slavic languages. It is currently thought to be the second-most widely spoken conlang in the world, after Esperanto, with approx. 7,000 speakers. Unlike Esperanto, of course, it aims to be a more naturalistic language. Wikipedia describes it as “essentially a modern continuation of Old Church Slavonic, but also [drawing] on the various improvised language forms Slavs have been using for centuries to communicate with Slavs of other nationalities”.
In choosing vocabulary, Interslavic seeks to identify the most common/most recognisable word across all Slavic languages, and goes with that one. The inflections are largely regular, and are based on a simplified “greatest common denominator” across Slavic languages, but some variation is tolerated and there are a small number of irregular verbs (byti “to be”, dati “to give”, jěsti “to eat”, věděti “to know”, idti “to walk, to go by foot”), which I’m assuming are irregular in a way that’s common across most of the Slavic languages.
Interslavic nouns can have three genders (masculine, feminine and neuter), two numbers (singular and plural) and six noun cases (nominative, accusative, genitive, dative, instrumental, locative). Nouns can belong to 4 or 5 declensions (depending on whether the speaker has kept the fifth declension from Old Church Slavonic or merged those nouns into one of the other ones like most modern Slavic languages have done), which determines the pattern by which all the other inflections occur.
Adjectives can be “hard” or “soft”, depending on the stem, which results in minor differences to their inflections that some writers ignore (instead inflecting all adjectives as hard or all as soft).
Verbs can belong to one of two conjugations, and have up to two stems. The first stem is used for the infinitive, past tense, conditional mood, past passive participle and verbal noun. The second stem is used for the present tense, the imperative and the present active participle. For most verbs, the two stems are the same; for most of the remainder, the second can be derived regularly from the first; for a small number of verbs, the two stems must both be memorised. Like in the Slavic languages generally, Interslavic verbs inflect differently for the perfect and imperfect aspects.
Interslavic can be written equally in the Cyrillic or Latin alphabet. The letters don’t line up 1:1 like they do in Serbo-Croatian, but instead there are some Cyrillic letters that are written with a digraph in Latin. For the Latin alphabet specifically, there’s also an “extended set” of letters with diacritics that some people may choose to use if they want to provide more information about a word’s etymology in Old Church Slavonic or Proto-Slavic.