Pets are allowed to travel on our trains.
In particular, small dogs, cats and other small pets (kept in dedicated containers of no larger than 70x30x50 cm) are allowed free of charge in first and second class of all the categories of trains. For trains operated with ETR 450 carriages, the cage/box must be held on your lap.
Only one box/cage is allowed per traveller. 

For individual travellers, a dog of any size can travel (with a muzzle and leash):
on Espressi (Express), IC and ICN trains in both first and second class on regional trains in the aisles or platform of the last carriage, except for between
of 7 and 9 am in the morning on weekdays from Monday to Friday;In these cases for the transport of a dog you must buy a second class ticket at the price applied to the train, reduced by 50%. 

in the sleeping carriages, ordinary and comfort couchettes and in the Excelsior and Excelsior E4 carriages for whole compartments reserved. When travelling on couchette, WL or Excelsior, a 2nd class ticket for the express train must be purchased, with a reduction of 50%. 
The ticket of the accompanying adult must be bought and booked at the same time. 

At no time can the animals in the carriages occupy places reserved for other passengers. If any disturbance is caused to other travellers, the train staff may require that the accompanying adult and animal move to another place if available or alight from the train.
Guide dogs for the sight-impaired can travel on all trains free of charge and without any obligation. 

IMPORTANT:
All dog owners must have a dog registration certificate (or dog "passport" for travellers from outside Italy). You must produce this certificate when purchasing your animal's ticket, if applicable, and during transit. If found without a certificate on board, you will be fined and have to get off the train at the next stop.