My husband is self-employed. What is the maximum amount he can write off for tools?

[smarttees]

The limit is $5000 per invoice for this kind of stuff and there is a section 179 expense limit of $1 million. Read irs publication 535.

[SweetieJean]

Per Pub 535:

Unless the uniform capitalization rules apply, amounts spent for tools used in your business are deductible expenses if the tools have a life expectancy of less than 1 year or they cost $200 or less per item or invoice. 

As with all other business expenses:

To be deductible, a business expense must be both ordinary and necessary. An ordinary expense is one that is common and accepted in your industry. A necessary expense is one that is helpful and appropriate for your trade or business. An expense does not have to be indispensable to be considered necessary

[Hal_Al]

There is no monetary  limit on how much he can deduct.  As the other replies indicate, there are rules on whether expensive tools can be written off, totally, in the year purchased or whether the cost must be spread  out (depreciated) over several tears (typically 5 years or 7 years)