As the Utah Legislature opens its annual 45-day session Monday, the atmosphere seems more calm - at least to begin with - than it was last year when a bitter fight over school finances was brewing. But there are plenty of tough issues to face.

Money will be a problem, as usual, although Gov. Norm Bangerter's budget calls for spending an additional $150 million - without any tax increase. Both real and perceived needs are vastly greater than all available revenue, yet that is always the case.Financing of human services is going to once again be an exercise in heartbreak as the apparent needs outstrip the state's ability to provide everything that ought to be done.

Educators want more than the governor is offering in his budget - a 5 percent increase in school spending - but there is no strike threat like there was last year, and there will be no fractious direct confrontation with lawmakers.

Despite gaining average salary hikes of 6 percent or more last year, the most significant in several years, teachers came away from the bitter fight with some injury to their image and prestige. They don't want a repeat and are planning a more low-key lobbying effort.

However, absence of confrontation over schools doesn't mean the Legislature won't have conflict. Other issues lurking in the wings could cause some potentially explosive political fights.

While Republicans continue to control both houses of the Legislature, Democrats did make some gains in the November elections, and party leaders say they plan to be more aggressive in pushing their own political agenda this time around, particularly in the areas of taxes and schools.

There are other tough problems facing lawmakers. One of the top issues is the need to restructure the property-tax system in the aftermath of a court case that ruled Utah had not fairly taxed AMAX Corp. property. More than two dozen other multi-county businesses are prepared to file lawsuits on the same grounds. At risk is $55 million in property taxes. That money is necessary to balance Bangerter's 1991-92 budget.

Unless the tax question is resolved, the $55 million in property taxes will be added to locally assessed business and homes, causing an average 7 percent increase in everybody's property taxes. One option being considered is to levy new kinds of taxes against multicounty firms like AMAX. But nearly every suggested option has its drawbacks.

How this problem is handled may be the most important fiscal issue in the entire session. Answers won't be easy to find, and whatever lawmakers decide may be subject to further legal challenges.

The most emotional question on the agenda will probably be abortion. A state task force has produced a bill to toughen Utah abortion laws. The key issue is how strict such a law should be and whether it would stand a chance of being upheld on constitutional grounds.

Bangerter, while he wants further restrictions on abortion, may prefer something less restrictive than the task force measure being proposed. The governor says he doesn't want a bill that will involve a costly and unsuccessful fight in federal courts. The debate is sure to be intense.

Other significant issues facing lawmakers include proposed changes in the state constitution for selection of members of the State School Board. One proposal calls for prospective candidates to be screened by a committee before running for election. There will be bills on campaign reform and conflict-of-interest affecting legislators. Such legislation is long overdue.

Some kind of change in the income tax system may emerge during the session. It is long overdue. Because Utah tax brackets have been unchanged for so many years, the state essentially has come to have a flat tax with nearly everyone in the highest category. At least a start should be made on a more equitable system.

The 1991 session promises to be filled with some crucial issues that are going to demand statesmanship, patience, understanding and skill. Let's hope Utah lawmakers, in all their diversity, can rise to the challenge.