IRPEF: state taxes on your personal income. The tax quota increases with salary, from 23% to 43%.
IRES: state taxes on businesses (24%).
IRAP: regional taxes (3.9%).
IRI: a businessman can choose to pay for the next 5 years her/his salary taxes at the same quota then the business IRES taxes (24%), by betting that it will be lower than her normal IRPEF quota.
IVA: (value added tax) is paid/deduced on services and goods sold/bought by the business. The tax quota is normally 22% except for some goods/services (4% and 10%).
It is important to check carefully and to get help, as rules often change.
It is not easy to summarize Italian fiscal system, these are only some basic hints about 2019 fiscal laws:
Personal taxes summary for incomes in fiscal year 2018: https://www.pmi.it/impresa/contabilita-e-fisco/52519/irpef-scaglioni-e-aliquote.html
But, if you start a new business, opening a “Partita IVA” with a simplified accountancy system, you can choose not to pay IRES but a so-called “flat tax” which usually allows you to pay less: https://www.informazionefiscale.it/partita-iva-2019-nuove-regole-novita