The nouns are of course essential for studying the Georgian grammar. The basics of singular and plural are comparatively easy to learn, but of course, practice makes the master. The same is true about the seven cases (ბრუნვა) in Georgian, which are summarized below. Consult the referenced text books for more details. The word ბრუნვა literally means twist, turn, run // die Drehung, die Wendung, der Lauf.
The Singular (Nominative Case)
The Georgian noun (არსებითი სახელი) can often be recognized by ending on -ი, for example სახლი - the house, ცხენი - the horse. The nominative case (სახელობითი ბრუნვა) is used just as it is in English or German: სახლი - the house // das Haus.
The Plural
The usual plural ending in Georgian is -ები (e.g. კაცები, სახლები, ცხენები), which is not applied when giving the specific number of the item (ორი კაცი, ორი სახლი, სამი ცხენი). Very rare in contemporary Georgian is the antique plural which is sometimes used in order to give words a historical touch or some official sounding (and in old texts, of course). This antique plural or old plural, which still finds some use in contemporary Georgian, can be recognized by the suffix -ნი (nominative case), e.g. კაცნი - the men, ორნი - the two (singular ორი) or ისინი - they (singular ის) or ობობასნაირნი - the Arachnids (singular ობობასნაირი). Note that the plural marker -ნი changes to -თა in the ergative, dative and genitive cases, e.g. კაცთა სახელები - the men's names. And in the vocative case the antique plural is -ნო: კაცნო! Hey, you men!
More on the nominative case in Tschenkeli (1958) 1. Lektion p. 4. Abuladze & Ludden (2006) §§1-20, p. 179-184. Hewitt (2005) Chapter 1 p. 24.
The Genitive Case
The genitive case (ნათესაობითი ბრუნვა) is used in Georgian much like in English and in German and is marked with the suffix -ის: გიორგის სახლი - Giorgi's house // Giorgis Haus. It is used both for persons and things as well (წიგნის ფერი - the book's color // die Farbe des Buches).
The Georgian genitive is also used for what are combined words and expression of materials in English and German: წიგნის სათაური - book title // Buchtitel (literally: the book's title) or ხის სახლი - stone house // Steinhaus (literally: the rock's house). With some practice using the genitive in Georgian should be quite easy.
More on the genitive in Tschenkeli (1958) 1. Lektion p. 5. Abuladze & Ludden (2006) §§1-20, p. 179-184. Hewitt (2005) Chapter 2, p. 42.
The Dative Case
In Georgian the dative case (მიცემითი ბრუნვა) often marks the object in a sentence, combining both the true dative (whom? // Wem?) and the accusative (who? what? // Wer? Was?). The usual marker for the dative is the suffix -ს. Since this often combines both the direct and the indirect object, it might take some time and practice distinguishing both in a Georgian sentense: ვგზავნი მას წერილს - I am sending him (მას) a letter (წერილს).
More on the dative in Tschenkeli (1958) 1. Lektion, p. 5. Abuladze & Ludden (2006) §§1-20, p. 179-184. Hewitt (2005) Chapter 2, p. 40.
The Instrumental Case
The instrumental case (instrumentalis, მოქმედებითი ბრუნვა) is used when expressing that something is done with or using something. The word for the used tool is marked with the suffix -ით, e.g. ვაკეთებ იმას ჩაქუჩით - I am doing this with the hammer.
The Intstrumental is also used when marking a point in time, similar to the Dative but emphasizing that the action is done usually at this time or for a certain time period: დილას (Dative, at the morning) and დილით (Instr., usually at the morning).
I know of only one Georgian verb that is used with the instrumentalis instead of the usual dative: ის სარგებლობს ქაღალდით - he uses paper.
The instrumental is called მოქმედებითი ბრუნვა in Georgian, from მოქმედება - movement // die Bewegung.
More on the instrumental in Tschenkeli (1958) 1. Lektion p. 6. Abuladze & Ludden (2006) §§1-20, p. 179-184. Hewitt (2005) Chapter 3, p. 59.
The Adverbial Case
In order to emphasize the function of someone or something in a sentence, the instrumental case (ვითარებითი ბრუნვა) is used. The word specifying this function is often marked with the suffix -ად: მე ვხმარობ ამ ფურცელს წერილად - I am using this paper slip as a letter.
The name ვითარებითი ბრუნვა for the adverbial case comes from the word ვითარება - position, situation, condition // die Lage, die Situation, der Zustand.
More on the adverbial case in Tschenkeli (1958) 1. Lektion, p. 7. Abuladze & Ludden (2006) §§1-20, p. 179-184. Hewitt (2005) Chapter 4, p. 81.
The Ergative Case
The ergative case (მოთხრობითი ბრუნვა) is a specialty in the Georgian language, marking the subject in the aorist tense and the optative and imperative moods with the suffix -მ or -მა: ქალმა დაწერა წერილი - the woman wrote the letter. მან უნდა ისწავლოს! He should learn!
Some rare verbs also demand the Ergative for their subject even in the present tense, e.g. იცის: ქალმა იცის გზა - the woman knows the way.
More on the ergative in Tschenkeli (1958) §2, p. 2, Lektionen 18-19, p. 150ff.. Abuladze & Ludden (2006) §§1-20, p.179-184 . Hewitt (2005) p. Chapter 8, p. 137.
The Vocative Case
The Georgian language knows a certain vocative case (წოდებითი ბრუნვა), which is used when directly addressing someone. Often this is done by simply omitting the suffix -ი from the Nominative: შამილ! (instead of შამილი - Shamil), ლევან! (instead of ლევანი). In other cases, the -ი stays because it belongs to the word root: ირაკლი! გიორგი!
Most often the Vocative marker is the suffix -ო, as in კაცო! Hey, man!; ბიჭო! Hey, boy! or ბავშვებო! Hey, children! as teachers and professors often address their students in school or at the university. In longer words with more syllables, the vocative marker -ო changes to -ვ. In some older texts or songs one can find the -ვ simply being attached to a word, e.g. when the girl in the famous song აპარეკა adresses him with აპარეკავ! - Hey, abrek!
In a third variant of the vocative it is the typical abbreviation of the normal form which lets a person know, he or she is being directly addressed, e.g. when the Georgian students address their მასწავლებელი (teacher) jovially with მასწ! Hey, teacher! (See this example in the Reading material!)
Sometimes the word itself is accommodated or shortend to end on -ო, e.g. ელისაბედ! is often shortened to ელისო! when addressing a woman with this name, especially among friends and family members, same with გიო! instead of გიორგი!
In short, the Vocative should be easy to learn but there are some exceptions to be considered. Just keep your ears open how people address each other and you will be fine!
More on the Vocative in Tschenkeli (1958) p. 4. Abuladze & Ludden (2006) §16, p. 181. Hewitt (2005) Chapter 7, p. 130.