For classical singers it’s really important to build up a good foundation of vocal technique, breathing, sound projection, vocal attack, coloratura, phrasing and many other technical tools. Undoubtedly, one of the best ways to achieve this goal is to practice vocal exercises or so called, vocalises during your singing lessons. Here below I have listed links to the vocal exercises/ vocalises which are most popular and efficient in the world of classical singing. Have patience and explore them while you are on the path of making your voice better. Patience is needed. Some of them are written for low voices, some of them are written for high voices. Some can be applied to any voice. Don’t rush, take step-by-step, make yourself familiar with the melody, find vocal accompaniment online, nowadays it’s so easy, for example, on YouTube. Try to listen to other singers who are singing the same piece.
After singing 4 to 6 exercises, for sure, you will start to gain confidence, sensation of security and good sound projection. Additionally, you will start to extend your musical horizons, because , normally, vocalises are written in different tempo, with different vocal range (normally, it’s becoming bigger, once you are progressing)etc. If you want to make your singing lessons indeed efficient, trust me, vocalises are extremely important.
Theoretical and Practical Vocal Method, Op 31 (Méthode de chant théorique et pratique, Op.31) (Marchesi, Mathilde) https://imslp.org/wiki/Méthode_de_chant_théorique_et_pratique%2C_Op.31_(Marchesi%2C_Mathilde)