It depends on your objectives for assessing soil quality. As soil quality is nothing but fitness of soil to the specified purpose, therefore, it will vary depending on the purpose. Several numbers of literature are available for this topic. However if you are interested to assess soil quality for food production or ecosystem point of view, then I suggest the following research papers for your reference.

Mandal, D., Singh, R., Dhyani, S.K. and Dhyani, B.L.2010. Landscape and land use effects on soil resources in a Himalayan watershed. Catena, 81 : 203-208.

Andrews, S.S., Carroll, C.R., 2001. Designing a decision tool for sustainable agro ecosystem management: soil quality assessment of a poultry litter management case study. Ecol. Appl. 11, 1573–1585.

Andrews, S.S., Karlen, D.L., Mitchell, J.P., 2002. A comparison of soil quality indexing methods for vegetable production systems in northern California. Agric. Ecosyst. Environ. 90, 25–45

Dear Sir, Here are few very popular and valuable links which could help you.

http://www.sciencedirect.com/science/article/pii/S0038071704003785

http://www.sciencedirect.com/science/article/pii/S0167880903000859

https://dl.sciencesocieties.org/publications/sssaj/abstracts/57/3/SS0570030743

http://www.sciencedirect.com/science/article/pii/S0167880901002547

With best regards

Dear Nguyen Hue,

In general soil quality, is a very complex term, it included the majority of the factor responsible for the proper functioning of the soil system. There should be proper analysis of the physical like ,water holding capacity, bulk density, EC,CEC, chemical like soil pH, C,N,P,K, C:N ratio, dissolved organic carbon,enzymatic profiling, and biological analysis for nitrifiers, denitrifiers, methanotrophs, eubacteria,AMF and other fungi. there sholud be proper identification of the other flora like various Earthworms, Microarthropods, Nematodes, Protozoa etc.

In core matrix people are more focused towards the, water holding capacity,bulk density,CEC, pH,EC, SMBC,and  C,N,P, K analysis..

However It will solely depends upon your objectives.  

Dear Nguyen,

indeed, as mentioned before, much depends on your objectives, but you are likely to find a similar suite of physical, chemical, and biological parameters reported in multiple studies. A good overview of the topic can be found in Karlen et al. 2004 (in: Managing Soil Quality), additional interesting papers might be Shukla et al. 2004 (also provides critical levels of values), Ball et al. 2007 (rates structural quality), Mueller et al. 2013 or the USDA NRCS overview of on-site soil quality indicators.

Good luck!

As indicated by the previous comments, to a large degree it will depend on what you are interested. In spite of that, it is fair to say that probably the most important factor is soil organic carbon (~soil organic matter).  This is because it integrates and is intimately associated with many other soil parameters, i.e., nutrient availability, bulk density, water holding capacity, microbial activity, CEC, etc) and more often than not tells us a lot about the climate and vegetation production also

All the previous considerations for soil quality assessment are quite applicable and important. I re-iterate the comment regarding deciding what type of function one is to assess for the particular landscape. Restoration to a natural ecosystem will likely be differently assessed (using a different set of parameters) than if one is designing a sustainable cropping system. Again the key parameter is soil organic C (or soil organic matter), however, because buildup of SOC requires considerable time, one might consider measuring more labile pools including active C and/or water-extractable organic C. Some biological parameters that are quickly measured and are fairly rapidly responsive to management include soil enzymatic activity (i.e., glucosidase, phosphatase), and various groups measured for example by PLFA (total fungi, bacteria [gram neg, gram pos, actinobacteria), mycorrhizae, and various ratios as indicators of balance and stress.

Indeed evaluation of soil health (or soil quality) is a beneficial tool for sustainable soil management. There are 4 types of indices for this purpose: visual signs (such as erosion rills, yellowing of the leaves, etc.), soil physical parameters (such as water holding capacity, texture, structure, etc), soil chemical properties (such as EC, pH, CEC, etc) and soil biological properties (such as respiration, earthworm population, respiration, etc.). There are hundreds of parameters to choose from. However, the minimum data set or the appropriate selection of the parameters depends on: climate of the location,objective, time and budget, specific problems in an area, the ease of measurement techniques, availability of equipments... A good evaluation and monitoring scheme, should consider all 4 groups of parameters mentioned above, to get an overall view of the soil health condition of the field. Organic matter is an excellent parameter and in my opinion is a must, since it affects soil physical, chemical and biological properties. However it is not enough and some other parameters from each categories should also be included. So the minimum number really depends on your purpose (agronomic, environmental, engineering, ... ) and local conditions (climate, agronomic problems, major soil problems, i.e. salinity, acidity, etc.). However, soil quality (or soil health) evaluations by scientists, usually  5-6 parameters are chosen that covers all categories mentioned above.

Regarding the soil physical quality indicators, I suggest also the following papers:

http://onlinelibrary.wiley.com/doi/10.1111/sum.12137/abstract

http://onlinelibrary.wiley.com/doi/10.1002/ldr.2263/abstract

https://www.soils.org/publications/sssaj/abstracts/75/5/1958

http://www.sciencedirect.com/science/article/pii/S0016706109001967

http://pubs.aic.ca/doi/abs/10.4141/cjss2013-097

Parameters should be considered when evaluating soil quality are:-

1. Water holding capacity

2. Bulk Density

3. Soil organic matter

4. Microbial Activity

5. Soil chemical Properties(i.e EC, CEC, pH etc.)

6. oiliness of soil(that oppose the absorbtion of water