Allegiant Air is a budget airline that primarily operates in the United States. They offer flights to various destinations and focus on providing low-cost travel options. To find and book Allegiant airline tickets, you can follow these steps:

• Visit Allegiant Air's official website: Go to www.allegiantair.com.
• Search for flights: Enter your departure city, destination, travel dates, and the number of passengers. Click on the "Search" button to view available flights.
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• Review flight options: The website will display a list of flights that match your search criteria. You can compare different options based on flight times and prices.
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• Select your flight: Once you find a suitable flight, click on it to view more details. Make sure to check the fare rules and any additional fees that may apply.
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• Add extras (optional): allegiant airline tickets offer additional services like seat selection, baggage allowance, and in-flight amenities. You can customise your booking by adding these extras if needed.
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• Complete the booking: After reviewing your flight details and optional extras, proceed to the booking and payment process.

Please note that Allegiant Air is a budget airline, and they may have specific policies and procedures that differ from full-service carriers. Be sure to read their terms and conditions, baggage policies, and any other relevant information before finalising your booking.

As my information might be outdated, I recommend visiting Allegiant Air's website or contacting their customer support for the most up-to-date and accurate information on booking tickets and their current offerings.