Overlay is a classic operation performed by most GIS and point-in-area overlay is, perhaps, the most widely used spatial operator. It is surprising, therefore, that remarkably few users are aware of how the overlay operator computes new geometries, changes geometry types, and/or calculates new attribute values.  
Task Your task is to demonstrate overlay operators using ArcGIS by complete the exercise on Transformations and Descriptive Summaries.
Buffering, point-in-polygon and polygon overlay
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Source: ESRI Virtual Campus, 2005. Module 4 in Turning Data Into Information.
Task Overlay can be implemented on both raster and vector data models. The former are simple to compute once the data have been resampled to a common spatial support but possibly lack the intuitive approach of vector operations. Your task is to assess how overlay operators work on raster and vector data models by using the interactive demonstrations.
Raster Overlay
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Source: Klinkenberg B, 2006. Simple demonstrations of fundamental GIS operations: binary overlays. <http://www.geog.ubc.ca/courses/klink/java/java_examples.html> URL last accessed 08-01-2007.
Vector Overlay
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Source: Ellis F, 2001. Vector overlay: point- and line- in-polygon, in GIS Self Learning Tool, University of Melbourne. <http://www.sli.unimelb.edu.au/gisweb/VOModule/VOModule.htm> URL last accessed 08-01-2007.
Task Your task is to review the following documents and explain how overlay operators work on raster and vector data models. You should complete the e-tutorials.
Overlay Analysis: Points & Lines in Areas
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Source: Trodd N, 2005. Overlay analysis: points and lines in areas.

This document includes an e-tutorial on line intersection.

Point-in-Polygon: Simple Algorithm Source: Wise S, 2002. Ch 4 section 3 in GIS Basics. London: Taylor and Francis.
Vector Algorithms for Lines Source: Wise S, 2002. Ch 3 in GIS Basics. London: Taylor and Francis.
Overlay Analysis: Areas and Surfaces
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Source: Trodd N, 2005. Overlay analysis: areas and surfaces.

e-Tutorial: Crosstabulation
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Can you solve the problem posed in the CROSSTAB and reclassification demonstration?
Polygon Overlay
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Source: NCGIA, 1997. The polygon overlay operation, in Core Curriculum in GIScience. <http://www.ncgia.ucsb.edu/giscc/units/u186/u186.html> URL last accessed 01/05.
Task Your task is to identify some of the issues that affect the implementation of overlay operators. We can separate these into issues that affect the computation of geometries and issues that affect the calculation of new attibutes. If you get excited by sliver polygons then read the article by Klajnsek and Zalik (2005) to see what can be done with really messy polygons. The other two articles give examples of weighted overlay.
Merging Polygons
[ ScienceDirect ] [ pdf ]
Source: Klajnsek G and Zalik B, 2005. Merging polygons with uncertain boundaries. Computers & Geosciences, 31, 353359.
Landslide Hazard Analysis
[ ScienceDirect ] [ pdf ]
Source: Chau KT, Sze YL, Fung MK, Wong WY, Fong EL and Chan LCP, 2004. Landslide hazard analysis for Hong Kong using landslide inventory and GIS. Computers & Geosciences, 30, 429443.
Urban Land-Use Allocation
[ ScienceDirect ] [ pdf ]
Source: Svoray T, Pua Bar (Kutiel) & Bannet T, 2005. Urban land-use allocation in a Mediterranean ecotone: Habitat Heterogeneity Model incorporated in a GIS using a multi-criteria mechanism. Landscape and Urban Planning, 72, 337351.